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向量组的秩与最大无关组",[1096,1463,1464],{},[1105,1465,1468],{"href":1466,"rel":1467},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100545185",[1109],"线性代数学习笔记——第四十七讲——向量组的秩与最大无关组的概念",[1096,1470,1471],{},[1105,1472,1475],{"href":1473,"rel":1474},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100545450",[1109],"线性代数学习笔记——第四十八讲——矩阵的列秩和行秩",[1096,1477,1478],{},[1105,1479,1482],{"href":1480,"rel":1481},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100545669",[1109],"线性代数学习笔记——第四十九讲——向量组之间的线性表出和秩",[1096,1484,1485],{},[1105,1486,1489],{"href":1487,"rel":1488},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100545879",[1109],"线性代数学习笔记——第五十讲——最大无关组的性质和等价叙述",[1096,1491,1492],{},[1099,1493,1494],{},"§4.4. 线性方程组解的结构",[1096,1496,1497],{},[1105,1498,1501],{"href":1499,"rel":1500},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100563945",[1109],"线性代数学习笔记——第五十一讲——n维向量空间的基、维数与坐标",[1096,1503,1504],{},[1105,1505,1508],{"href":1506,"rel":1507},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100564018",[1109],"线性代数学习笔记——第五十二讲——齐次方程组解的性质和基础解系",[1096,1510,1511],{},[1105,1512,1515],{"href":1513,"rel":1514},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100564726",[1109],"线性代数学习笔记——第五十三讲——齐次方程组求解实例",[1096,1517,1518],{},[1105,1519,1522],{"href":1520,"rel":1521},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100568940",[1109],"线性代数学习笔记——第五十四讲——非齐次方程组解的性质",[1096,1524,1525],{},[1105,1526,1529],{"href":1527,"rel":1528},"https:\u002F\u002Fmp.csdn.net\u002Fpostedit\u002F100569281",[1109],"线性代数学习笔记——第五十五讲——非齐次方程组求解实例",[1204,1531,1533],{"id":1532},"第五章特征值与特征向量","第五章——特征值与特征向量",[1096,1535,1536],{},[1099,1537,1538],{},"§5.1 特征值与特征向量的概念与计算",[1096,1540,1541],{},[1105,1542,1545],{"href":1543,"rel":1544},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100584392",[1109],"线性代数学习笔记——第五十六讲——特征值及特征向量的定义",[1096,1547,1548],{},[1105,1549,1552],{"href":1550,"rel":1551},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100584678",[1109],"线性代数学习笔记——第五十七讲——特征子空间",[1096,1554,1555],{},[1105,1556,1559],{"href":1557,"rel":1558},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100584921",[1109],"线性代数学习笔记——第五十八讲——特征值与特征向量的判定",[1096,1561,1562],{},[1105,1563,1566],{"href":1564,"rel":1565},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100585358",[1109],"线性代数学习笔记——第五十九讲——特征值与特征向量的计算",[1096,1568,1569],{},[1105,1570,1573],{"href":1571,"rel":1572},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100585433",[1109],"线性代数学习笔记——第六十讲——特征多项式",[1096,1575,1576],{},[1105,1577,1580],{"href":1578,"rel":1579},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100654266",[1109],"线性代数学习笔记——第六十一讲——矩阵函数、逆矩阵、伴随矩阵的特征值与特征向量",[1096,1582,1583],{},[1099,1584,1585],{},"§5.2 矩阵的相似对角化",[1096,1587,1588],{},[1105,1589,1592],{"href":1590,"rel":1591},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100654621",[1109],"线性代数学习笔记——第六十二讲——矩阵的相似对角化引例",[1096,1594,1595],{},[1105,1596,1599],{"href":1597,"rel":1598},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100654919",[1109],"线性代数学习笔记——第六十三讲——相似的定义与性质",[1096,1601,1602],{},[1105,1603,1606],{"href":1604,"rel":1605},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100661294",[1109],"线性代数学习笔记——第六十四讲——相似对角化的判定（1）",[1096,1608,1609],{},[1105,1610,1613],{"href":1611,"rel":1612},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100662028",[1109],"线性代数学习笔记——第六十五讲——相似对角化的判定（2）",[1096,1615,1616],{},[1105,1617,1620],{"href":1618,"rel":1619},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100665386",[1109],"线性代数学习笔记——第六十六讲——矩阵方幂的计算",[1096,1622,1623],{},[1099,1624,1625],{},"§5.3 n维向量空间的正交性",[1096,1627,1628],{},[1105,1629,1632],{"href":1630,"rel":1631},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100669700",[1109],"线性代数学习笔记——第六十七讲——向量的内积",[1096,1634,1635],{},[1105,1636,1639],{"href":1637,"rel":1638},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100670303",[1109],"线性代数学习笔记——第六十八讲——柯西—施瓦兹（Cauchy-Schwarz）不等式",[1096,1641,1642],{},[1105,1643,1646],{"href":1644,"rel":1645},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100676734",[1109],"线性代数学习笔记——第六十九讲——正交向量组与标准正交基",[1096,1648,1649],{},[1105,1650,1653],{"href":1651,"rel":1652},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100677372",[1109],"线性代数学习笔记——第七十讲——格拉姆—施密特（Gram-Schmidt）正交化方法",[1096,1655,1656],{},[1105,1657,1660],{"href":1658,"rel":1659},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100677838",[1109],"线性代数学习笔记——第七十一讲——正交矩阵",[1096,1662,1663],{},[1105,1664,1667],{"href":1665,"rel":1666},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100708919",[1109],"线性代数学习笔记——第七十二讲——共轭矩阵",[1096,1669,1670],{},[1099,1671,1672],{},"§5.4 实对称矩阵的相似对角化",[1096,1674,1675],{},[1105,1676,1679],{"href":1677,"rel":1678},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100715687",[1109],"线性代数学习笔记——第七十三讲——实对称矩阵的特征值与特征向量",[1096,1681,1682],{},[1105,1683,1686],{"href":1684,"rel":1685},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100715880",[1109],"线性代数学习笔记——第七十四讲——实对称矩阵的相似对角化",[1204,1688,1690],{"id":1689},"第六章二次型与二次曲面","第六章——二次型与二次曲面",[1096,1692,1693],{},[1099,1694,1695],{},"§6.1. 实二次型",[1096,1697,1698],{},[1105,1699,1702],{"href":1700,"rel":1701},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100750410",[1109],"线性代数学习笔记——第七十五讲——二次型及其矩阵表示",[1096,1704,1705],{},[1105,1706,1709],{"href":1707,"rel":1708},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100751105",[1109],"线性代数学习笔记——第七十六讲——矩阵的合同",[1096,1711,1712],{},[1105,1713,1716],{"href":1714,"rel":1715},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100751420",[1109],"线性代数学习笔记——第七十七讲——用配方法化二次型为标准型",[1096,1718,1719],{},[1105,1720,1723],{"href":1721,"rel":1722},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100751854",[1109],"线性代数学习笔记——第七十八讲——用正交变换化二次型为标准型",[1096,1725,1726],{},[1099,1727,1728],{},"§6.2. 正定二次型",[1096,1730,1731],{},[1105,1732,1735],{"href":1733,"rel":1734},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100752201",[1109],"线性代数学习笔记——第七十九讲——正定二次型的概念",[1096,1737,1738],{},[1105,1739,1742],{"href":1740,"rel":1741},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100752518",[1109],"线性代数学习笔记——第八十讲——正定二次型的性质（1）",[1096,1744,1745],{},[1105,1746,1749],{"href":1747,"rel":1748},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100780293",[1109],"线性代数学习笔记——第八十一讲——正定二次型的性质（2）",[1096,1751,1752],{},[1105,1753,1756],{"href":1754,"rel":1755},"https:\u002F\u002Fblog.csdn.net\u002Fhpdlzu80100\u002Farticle\u002Fdetails\u002F100780570",[1109],"线性代数学习笔记——第八十二讲——二次型的其它类型",[1096,1758,1759],{},"一些总结，可能较零碎。",[1761,1762],"hr",{},[1096,1764,1765],{},"本节是线代某些知识点总结，可能较零碎。",[1096,1767,1768,1769,1774],{},"对于简单的知识点，例如\"两行对应成比例，",[1105,1770,1773],{"href":1771,"rel":1772},"https:\u002F\u002Fso.csdn.net\u002Fso\u002Fsearch?q=%E8%A1%8C%E5%88%97%E5%BC%8F&spm=1001.2101.3001.7020",[1109],"行列式","为0\"就不讲了。暂时不举例题，有时间会继续补充！",[1091,1776,1778],{"id":1777},"一-初等行列变换","一. 初等行\u002F列变换",[1780,1781,1783],"h3",{"id":1782},"_1-计算行列式时行列变换都可","1. 计算行列式时，行列变换都可",[1096,1785,1786,1787,1910],{},"因为 ",[1788,1789,1792,1827],"span",{"className":1790},[1791],"katex",[1788,1793,1796],{"className":1794},[1795],"katex-mathml",[1797,1798,1800],"math",{"xmlns":1799},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1801,1802,1803,1822],"semantics",{},[1804,1805,1806,1810,1814],"mrow",{},[1807,1808,1809],"mi",{},"D",[1811,1812,1813],"mo",{},"=",[1815,1816,1817,1819],"msup",{},[1807,1818,1809],{},[1807,1820,1821],{},"T",[1823,1824,1826],"annotation",{"encoding":1825},"application\u002Fx-tex","D=D^{T}",[1788,1828,1832,1859],{"className":1829,"ariaHidden":1831},[1830],"katex-html","true",[1788,1833,1836,1841,1847,1852,1856],{"className":1834},[1835],"base",[1788,1837],{"className":1838,"style":1840},[1839],"strut","height:0.6833em;",[1788,1842,1809],{"className":1843,"style":1846},[1844,1845],"mord","mathnormal","margin-right:0.0278em;",[1788,1848],{"className":1849,"style":1851},[1850],"mspace","margin-right:0.2778em;",[1788,1853,1813],{"className":1854},[1855],"mrel",[1788,1857],{"className":1858,"style":1851},[1850],[1788,1860,1862,1866],{"className":1861},[1835],[1788,1863],{"className":1864,"style":1865},[1839],"height:0.8413em;",[1788,1867,1869,1872],{"className":1868},[1844],[1788,1870,1809],{"className":1871,"style":1846},[1844,1845],[1788,1873,1876],{"className":1874},[1875],"msupsub",[1788,1877,1880],{"className":1878},[1879],"vlist-t",[1788,1881,1884],{"className":1882},[1883],"vlist-r",[1788,1885,1888],{"className":1886,"style":1865},[1887],"vlist",[1788,1889,1891,1896],{"style":1890},"top:-3.063em;margin-right:0.05em;",[1788,1892],{"className":1893,"style":1895},[1894],"pstrut","height:2.7em;",[1788,1897,1903],{"className":1898},[1899,1900,1901,1902],"sizing","reset-size6","size3","mtight",[1788,1904,1906],{"className":1905},[1844,1902],[1788,1907,1821],{"className":1908,"style":1909},[1844,1845,1902],"margin-right:0.1389em;","，所以不论动行\u002F列都是等价的。",[1912,1913,1914,1917],"blockquote",{},[1096,1915,1916],{},"变换规则：",[1918,1919,1920,2118,2121],"ol",{},[1921,1922,1923,1924,1955,1956,2080,2081,2109,2110,2113],"li",{},"\"倍乘\"：行列式的某行（列）乘某个元素 ",[1788,1925,1927,1941],{"className":1926},[1791],[1788,1928,1930],{"className":1929},[1795],[1797,1931,1932],{"xmlns":1799},[1801,1933,1934,1939],{},[1804,1935,1936],{},[1807,1937,1938],{},"k",[1823,1940,1938],{"encoding":1825},[1788,1942,1944],{"className":1943,"ariaHidden":1831},[1830],[1788,1945,1947,1951],{"className":1946},[1835],[1788,1948],{"className":1949,"style":1950},[1839],"height:0.6944em;",[1788,1952,1938],{"className":1953,"style":1954},[1844,1845],"margin-right:0.0315em;","。相应地，若行列式中某行（列）元素有公因子 ",[1788,1957,1959,1994],{"className":1958},[1791],[1788,1960,1962],{"className":1961},[1795],[1797,1963,1964],{"xmlns":1799},[1801,1965,1966,1991],{},[1804,1967,1968,1970,1974,1978,1980,1984,1988],{},[1807,1969,1938],{},[1971,1972,1973],"mtext",{}," ",[1811,1975,1977],{"stretchy":1976},"false","(",[1807,1979,1938],{},[1811,1981,1983],{"mathvariant":1982},"normal","≠",[1985,1986,1987],"mn",{},"0",[1811,1989,1990],{"stretchy":1976},")",[1823,1992,1993],{"encoding":1825},"k\\ (k\\neq 0)",[1788,1995,1997,2067],{"className":1996,"ariaHidden":1831},[1830],[1788,1998,2000,2004,2007,2010,2014,2017,2020,2064],{"className":1999},[1835],[1788,2001],{"className":2002,"style":2003},[1839],"height:1em;vertical-align:-0.25em;",[1788,2005,1938],{"className":2006,"style":1954},[1844,1845],[1788,2008,1973],{"className":2009},[1850],[1788,2011,1977],{"className":2012},[2013],"mopen",[1788,2015,1938],{"className":2016,"style":1954},[1844,1845],[1788,2018],{"className":2019,"style":1851},[1850],[1788,2021,2023,2057,2061],{"className":2022},[1855],[1788,2024,2026],{"className":2025},[1855],[1788,2027,2030],{"className":2028},[1844,2029],"vbox",[1788,2031,2034],{"className":2032},[2033],"thinbox",[1788,2035,2038,2042,2053],{"className":2036},[2037],"rlap",[1788,2039],{"className":2040,"style":2041},[1839],"height:0.8889em;vertical-align:-0.1944em;",[1788,2043,2046],{"className":2044},[2045],"inner",[1788,2047,2049],{"className":2048},[1844],[1788,2050,2052],{"className":2051},[1855],"",[1788,2054],{"className":2055},[2056],"fix",[1788,2058],{"className":2059},[1850,2060],"nobreak",[1788,2062,1813],{"className":2063},[1855],[1788,2065],{"className":2066,"style":1851},[1850],[1788,2068,2070,2073,2076],{"className":2069},[1835],[1788,2071],{"className":2072,"style":2003},[1839],[1788,2074,1987],{"className":2075},[1844],[1788,2077,1990],{"className":2078},[2079],"mclose","，则 ",[1788,2082,2084,2097],{"className":2083},[1791],[1788,2085,2087],{"className":2086},[1795],[1797,2088,2089],{"xmlns":1799},[1801,2090,2091,2095],{},[1804,2092,2093],{},[1807,2094,1938],{},[1823,2096,1938],{"encoding":1825},[1788,2098,2100],{"className":2099,"ariaHidden":1831},[1830],[1788,2101,2103,2106],{"className":2102},[1835],[1788,2104],{"className":2105,"style":1950},[1839],[1788,2107,1938],{"className":2108,"style":1954},[1844,1845]," 可提到行列式外面，即",[2111,2112],"br",{},[2114,2115],"img",{"alt":2116,"src":2117},"倍乘","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be10e4590.png",[1921,2119,2120],{},"\"互换\"：行列式中两行（列）互换，行列式变号。",[1921,2122,2123,2124,2152],{},"\"倍加\"：某行（列）的 ",[1788,2125,2127,2140],{"className":2126},[1791],[1788,2128,2130],{"className":2129},[1795],[1797,2131,2132],{"xmlns":1799},[1801,2133,2134,2138],{},[1804,2135,2136],{},[1807,2137,1938],{},[1823,2139,1938],{"encoding":1825},[1788,2141,2143],{"className":2142,"ariaHidden":1831},[1830],[1788,2144,2146,2149],{"className":2145},[1835],[1788,2147],{"className":2148,"style":1950},[1839],[1788,2150,1938],{"className":2151,"style":1954},[1844,1845]," 倍加到另一行（列），行列式不变。",[1780,2154,2156],{"id":2155},"_2-求矩阵的秩时行列变换都可","2. 求矩阵的秩时，行列变换都可",[1096,2158,2159],{},"因为初等变换不改变某个矩阵非零子式的最高阶数，秩指的就是非零子式的最高阶数。",[1912,2161,2162,2165,2205,2210],{},[1096,2163,2164],{},"初等变换的规则：",[1918,2166,2167,2170,2173],{},[1921,2168,2169],{},"\"倍乘\"：一个非零常数乘矩阵的某一行（列）。",[1921,2171,2172],{},"\"互换\"：互换矩阵中某两行（列）的位置。",[1921,2174,2175,2176,2204],{},"\"倍加\"：将矩阵的某一行（列）的 ",[1788,2177,2179,2192],{"className":2178},[1791],[1788,2180,2182],{"className":2181},[1795],[1797,2183,2184],{"xmlns":1799},[1801,2185,2186,2190],{},[1804,2187,2188],{},[1807,2189,1938],{},[1823,2191,1938],{"encoding":1825},[1788,2193,2195],{"className":2194,"ariaHidden":1831},[1830],[1788,2196,2198,2201],{"className":2197},[1835],[1788,2199],{"className":2200,"style":1950},[1839],[1788,2202,1938],{"className":2203,"style":1954},[1844,1845]," 倍加到另一行（列）。",[1096,2206,2207],{},[1099,2208,2209],{},"注意：",[1096,2211,2212,2213,2241,2242,2270,2271,2389],{},"某矩阵乘元素 ",[1788,2214,2216,2229],{"className":2215},[1791],[1788,2217,2219],{"className":2218},[1795],[1797,2220,2221],{"xmlns":1799},[1801,2222,2223,2227],{},[1804,2224,2225],{},[1807,2226,1938],{},[1823,2228,1938],{"encoding":1825},[1788,2230,2232],{"className":2231,"ariaHidden":1831},[1830],[1788,2233,2235,2238],{"className":2234},[1835],[1788,2236],{"className":2237,"style":1950},[1839],[1788,2239,1938],{"className":2240,"style":1954},[1844,1845],"，是矩阵中的每个元素都乘 ",[1788,2243,2245,2258],{"className":2244},[1791],[1788,2246,2248],{"className":2247},[1795],[1797,2249,2250],{"xmlns":1799},[1801,2251,2252,2256],{},[1804,2253,2254],{},[1807,2255,1938],{},[1823,2257,1938],{"encoding":1825},[1788,2259,2261],{"className":2260,"ariaHidden":1831},[1830],[1788,2262,2264,2267],{"className":2263},[1835],[1788,2265],{"className":2266,"style":1950},[1839],[1788,2268,1938],{"className":2269,"style":1954},[1844,1845],"，要与行列式区分。\n也就是 ",[1788,2272,2274,2311],{"className":2273},[1791],[1788,2275,2277],{"className":2276},[1795],[1797,2278,2279],{"xmlns":1799},[1801,2280,2281,2308],{},[1804,2282,2283,2286,2288,2291,2293,2295,2302,2304,2306],{},[1807,2284,2285],{"mathvariant":1982},"∣",[1807,2287,1938],{},[1807,2289,2290],{},"A",[1807,2292,2285],{"mathvariant":1982},[1811,2294,1813],{},[1815,2296,2297,2299],{},[1807,2298,1938],{},[1807,2300,2301],{},"n",[1807,2303,2285],{"mathvariant":1982},[1807,2305,2290],{},[1807,2307,2285],{"mathvariant":1982},[1823,2309,2310],{"encoding":1825},"|kA|=k^{n}|A|",[1788,2312,2314,2341],{"className":2313,"ariaHidden":1831},[1830],[1788,2315,2317,2320,2323,2326,2329,2332,2335,2338],{"className":2316},[1835],[1788,2318],{"className":2319,"style":2003},[1839],[1788,2321,2285],{"className":2322},[1844],[1788,2324,1938],{"className":2325,"style":1954},[1844,1845],[1788,2327,2290],{"className":2328},[1844,1845],[1788,2330,2285],{"className":2331},[1844],[1788,2333],{"className":2334,"style":1851},[1850],[1788,2336,1813],{"className":2337},[1855],[1788,2339],{"className":2340,"style":1851},[1850],[1788,2342,2344,2347,2380,2383,2386],{"className":2343},[1835],[1788,2345],{"className":2346,"style":2003},[1839],[1788,2348,2350,2353],{"className":2349},[1844],[1788,2351,1938],{"className":2352,"style":1954},[1844,1845],[1788,2354,2356],{"className":2355},[1875],[1788,2357,2359],{"className":2358},[1879],[1788,2360,2362],{"className":2361},[1883],[1788,2363,2366],{"className":2364,"style":2365},[1887],"height:0.6644em;",[1788,2367,2368,2371],{"style":1890},[1788,2369],{"className":2370,"style":1895},[1894],[1788,2372,2374],{"className":2373},[1899,1900,1901,1902],[1788,2375,2377],{"className":2376},[1844,1902],[1788,2378,2301],{"className":2379},[1844,1845,1902],[1788,2381,2285],{"className":2382},[1844],[1788,2384,2290],{"className":2385},[1844,1845],[1788,2387,2285],{"className":2388},[1844],"。",[1780,2391,2393],{"id":2392},"_3-解线性方程组时仅能使用初等行变换","3. 解线性方程组时，仅能使用初等行变换",[1096,2395,2396],{},"因为矩阵的每一种初等行变换都对应着线性方程组的同解变换，而作列变换会改变原来的方程。",[1096,2398,2399],{},[2114,2400],{"alt":2401,"src":2402},"解线性方程组","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1291006.png",[1780,2404,2406,2407,2503],{"id":2405},"_4-判定解的情况单纯求-rarabrarabrarab-的过程行列变换都可","4. 判定解的情况，单纯求 ",[1788,2408,2410,2450],{"className":2409},[1791],[1788,2411,2413],{"className":2412},[1795],[1797,2414,2415],{"xmlns":1799},[1801,2416,2417,2447],{},[1804,2418,2419,2422,2424,2426,2428,2431,2434,2436,2438,2440,2442,2445],{},[1807,2420,2421],{},"r",[1811,2423,1977],{"stretchy":1976},[1807,2425,2290],{},[1811,2427,1990],{"stretchy":1976},[1811,2429,2430],{"separator":1831},",",[1971,2432,2433],{}," ",[1807,2435,2421],{},[1811,2437,1977],{"stretchy":1976},[1807,2439,2290],{},[1811,2441,2430],{"separator":1831},[1807,2443,2444],{},"b",[1811,2446,1990],{"stretchy":1976},[1823,2448,2449],{"encoding":1825},"r(A),\\,r(A,b)",[1788,2451,2453],{"className":2452,"ariaHidden":1831},[1830],[1788,2454,2456,2459,2462,2465,2468,2471,2475,2479,2482,2485,2488,2491,2494,2497,2500],{"className":2455},[1835],[1788,2457],{"className":2458,"style":2003},[1839],[1788,2460,2421],{"className":2461,"style":1846},[1844,1845],[1788,2463,1977],{"className":2464},[2013],[1788,2466,2290],{"className":2467},[1844,1845],[1788,2469,1990],{"className":2470},[2079],[1788,2472,2430],{"className":2473},[2474],"mpunct",[1788,2476],{"className":2477,"style":2478},[1850],"margin-right:0.1667em;",[1788,2480],{"className":2481,"style":2478},[1850],[1788,2483,2421],{"className":2484,"style":1846},[1844,1845],[1788,2486,1977],{"className":2487},[2013],[1788,2489,2290],{"className":2490},[1844,1845],[1788,2492,2430],{"className":2493},[2474],[1788,2495],{"className":2496,"style":2478},[1850],[1788,2498,2444],{"className":2499},[1844,1845],[1788,2501,1990],{"className":2502},[2079]," 的过程行列变换都可",[1096,2505,2506,2509,2510,2567,2568,2615,2616,2648,2649,2677,2678,2706,2707,2750,2751,2807],{},[1099,2507,2508],{},"注","：将 ",[1788,2511,2513,2537],{"className":2512},[1791],[1788,2514,2516],{"className":2515},[1795],[1797,2517,2518],{"xmlns":1799},[1801,2519,2520,2534],{},[1804,2521,2522,2524,2526,2528,2530,2532],{},[1807,2523,2421],{},[1811,2525,1977],{"stretchy":1976},[1807,2527,2290],{},[1811,2529,2430],{"separator":1831},[1807,2531,2444],{},[1811,2533,1990],{"stretchy":1976},[1823,2535,2536],{"encoding":1825},"r(A,b)",[1788,2538,2540],{"className":2539,"ariaHidden":1831},[1830],[1788,2541,2543,2546,2549,2552,2555,2558,2561,2564],{"className":2542},[1835],[1788,2544],{"className":2545,"style":2003},[1839],[1788,2547,2421],{"className":2548,"style":1846},[1844,1845],[1788,2550,1977],{"className":2551},[2013],[1788,2553,2290],{"className":2554},[1844,1845],[1788,2556,2430],{"className":2557},[2474],[1788,2559],{"className":2560,"style":2478},[1850],[1788,2562,2444],{"className":2563},[1844,1845],[1788,2565,1990],{"className":2566},[2079]," 化行阶梯求秩时，往往我们需要",[1099,2569,2570,2571],{},"同时得到 ",[1788,2572,2574,2594],{"className":2573},[1791],[1788,2575,2577],{"className":2576},[1795],[1797,2578,2579],{"xmlns":1799},[1801,2580,2581,2591],{},[1804,2582,2583,2585,2587,2589],{},[1807,2584,2421],{},[1811,2586,1977],{"stretchy":1976},[1807,2588,2290],{},[1811,2590,1990],{"stretchy":1976},[1823,2592,2593],{"encoding":1825},"r(A)",[1788,2595,2597],{"className":2596,"ariaHidden":1831},[1830],[1788,2598,2600,2603,2606,2609,2612],{"className":2599},[1835],[1788,2601],{"className":2602,"style":2003},[1839],[1788,2604,2421],{"className":2605,"style":1846},[1844,1845],[1788,2607,1977],{"className":2608},[2013],[1788,2610,2290],{"className":2611},[1844,1845],[1788,2613,1990],{"className":2614},[2079],"，如果想用列变换的话，",[1099,2617,2618,2619,2647],{},"只能对 ",[1788,2620,2622,2635],{"className":2621},[1791],[1788,2623,2625],{"className":2624},[1795],[1797,2626,2627],{"xmlns":1799},[1801,2628,2629,2633],{},[1804,2630,2631],{},[1807,2632,2290],{},[1823,2634,2290],{"encoding":1825},[1788,2636,2638],{"className":2637,"ariaHidden":1831},[1830],[1788,2639,2641,2644],{"className":2640},[1835],[1788,2642],{"className":2643,"style":1840},[1839],[1788,2645,2290],{"className":2646},[1844,1845]," 单独列变换","，千万不要将 ",[1788,2650,2652,2665],{"className":2651},[1791],[1788,2653,2655],{"className":2654},[1795],[1797,2656,2657],{"xmlns":1799},[1801,2658,2659,2663],{},[1804,2660,2661],{},[1807,2662,2444],{},[1823,2664,2444],{"encoding":1825},[1788,2666,2668],{"className":2667,"ariaHidden":1831},[1830],[1788,2669,2671,2674],{"className":2670},[1835],[1788,2672],{"className":2673,"style":1950},[1839],[1788,2675,2444],{"className":2676},[1844,1845]," 列和 ",[1788,2679,2681,2694],{"className":2680},[1791],[1788,2682,2684],{"className":2683},[1795],[1797,2685,2686],{"xmlns":1799},[1801,2687,2688,2692],{},[1804,2689,2690],{},[1807,2691,2290],{},[1823,2693,2290],{"encoding":1825},[1788,2695,2697],{"className":2696,"ariaHidden":1831},[1830],[1788,2698,2700,2703],{"className":2699},[1835],[1788,2701],{"className":2702,"style":1840},[1839],[1788,2704,2290],{"className":2705},[1844,1845]," 的列混合运算，这样 ",[1788,2708,2710,2729],{"className":2709},[1791],[1788,2711,2713],{"className":2712},[1795],[1797,2714,2715],{"xmlns":1799},[1801,2716,2717,2727],{},[1804,2718,2719,2721,2723,2725],{},[1807,2720,2421],{},[1811,2722,1977],{"stretchy":1976},[1807,2724,2290],{},[1811,2726,1990],{"stretchy":1976},[1823,2728,2593],{"encoding":1825},[1788,2730,2732],{"className":2731,"ariaHidden":1831},[1830],[1788,2733,2735,2738,2741,2744,2747],{"className":2734},[1835],[1788,2736],{"className":2737,"style":2003},[1839],[1788,2739,2421],{"className":2740,"style":1846},[1844,1845],[1788,2742,1977],{"className":2743},[2013],[1788,2745,2290],{"className":2746},[1844,1845],[1788,2748,1990],{"className":2749},[2079]," 就不准了（但 ",[1788,2752,2754,2777],{"className":2753},[1791],[1788,2755,2757],{"className":2756},[1795],[1797,2758,2759],{"xmlns":1799},[1801,2760,2761,2775],{},[1804,2762,2763,2765,2767,2769,2771,2773],{},[1807,2764,2421],{},[1811,2766,1977],{"stretchy":1976},[1807,2768,2290],{},[1811,2770,2430],{"separator":1831},[1807,2772,2444],{},[1811,2774,1990],{"stretchy":1976},[1823,2776,2536],{"encoding":1825},[1788,2778,2780],{"className":2779,"ariaHidden":1831},[1830],[1788,2781,2783,2786,2789,2792,2795,2798,2801,2804],{"className":2782},[1835],[1788,2784],{"className":2785,"style":2003},[1839],[1788,2787,2421],{"className":2788,"style":1846},[1844,1845],[1788,2790,1977],{"className":2791},[2013],[1788,2793,2290],{"className":2794},[1844,1845],[1788,2796,2430],{"className":2797},[2474],[1788,2799],{"className":2800,"style":2478},[1850],[1788,2802,2444],{"className":2803},[1844,1845],[1788,2805,1990],{"className":2806},[2079]," 是准的）。",[1096,2809,2810],{},[2114,2811],{"alt":2812,"src":2813},"判定解的情况","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be11a1aaf.png",[1096,2815,2816],{},"但是，如果涉及到求通解或唯一解，那么就只能做行变换化行阶梯了，所以建议一开始就只做行变换。",[1912,2818,2819],{},[1096,2820,2821,2824,2825,2828],{},[1099,2822,2823],{},"总结","：求解的过程，就只进行",[1099,2826,2827],{},"初等行变换化行阶梯","求秩，并且顺势化为行最简型求解。",[1780,2830,2832],{"id":2831},"_5-求向量组极大无关组线性表出关系则仅行变换","5. 求向量组极大无关组、线性表出关系，则仅行变换",[1096,2834,2835,2836,2867,2868,3086,3087,3119],{},"因为初等行变换不改变列向量组的线性表出关系。例如下图，",[1788,2837,2839,2854],{"className":2838},[1791],[1788,2840,2842],{"className":2841},[1795],[1797,2843,2844],{"xmlns":1799},[1801,2845,2846,2851],{},[1804,2847,2848],{},[1807,2849,2850],{},"β",[1823,2852,2853],{"encoding":1825},"\\beta",[1788,2855,2857],{"className":2856,"ariaHidden":1831},[1830],[1788,2858,2860,2863],{"className":2859},[1835],[1788,2861],{"className":2862,"style":2041},[1839],[1788,2864,2850],{"className":2865,"style":2866},[1844,1845],"margin-right:0.0528em;"," 矩阵中 ",[1788,2869,2871,2910],{"className":2870},[1791],[1788,2872,2874],{"className":2873},[1795],[1797,2875,2876],{"xmlns":1799},[1801,2877,2878,2907],{},[1804,2879,2880,2888,2890,2897,2900],{},[2881,2882,2883,2885],"msub",{},[1807,2884,2850],{},[1985,2886,2887],{},"3",[1811,2889,1813],{},[2881,2891,2892,2894],{},[1807,2893,2850],{},[1985,2895,2896],{},"2",[1811,2898,2899],{},"+",[2881,2901,2902,2904],{},[1807,2903,2850],{},[1985,2905,2906],{},"1",[1823,2908,2909],{"encoding":1825},"\\beta_{3}=\\beta_{2}+\\beta_{1}",[1788,2911,2913,2977,3037],{"className":2912,"ariaHidden":1831},[1830],[1788,2914,2916,2919,2968,2971,2974],{"className":2915},[1835],[1788,2917],{"className":2918,"style":2041},[1839],[1788,2920,2922,2925],{"className":2921},[1844],[1788,2923,2850],{"className":2924,"style":2866},[1844,1845],[1788,2926,2928],{"className":2927},[1875],[1788,2929,2932,2959],{"className":2930},[1879,2931],"vlist-t2",[1788,2933,2935,2954],{"className":2934},[1883],[1788,2936,2939],{"className":2937,"style":2938},[1887],"height:0.3011em;",[1788,2940,2942,2945],{"style":2941},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1788,2943],{"className":2944,"style":1895},[1894],[1788,2946,2948],{"className":2947},[1899,1900,1901,1902],[1788,2949,2951],{"className":2950},[1844,1902],[1788,2952,2887],{"className":2953},[1844,1902],[1788,2955,2958],{"className":2956},[2957],"vlist-s","​",[1788,2960,2962],{"className":2961},[1883],[1788,2963,2966],{"className":2964,"style":2965},[1887],"height:0.15em;",[1788,2967],{},[1788,2969],{"className":2970,"style":1851},[1850],[1788,2972,1813],{"className":2973},[1855],[1788,2975],{"className":2976,"style":1851},[1850],[1788,2978,2980,2983,3026,3030,3034],{"className":2979},[1835],[1788,2981],{"className":2982,"style":2041},[1839],[1788,2984,2986,2989],{"className":2985},[1844],[1788,2987,2850],{"className":2988,"style":2866},[1844,1845],[1788,2990,2992],{"className":2991},[1875],[1788,2993,2995,3018],{"className":2994},[1879,2931],[1788,2996,2998,3015],{"className":2997},[1883],[1788,2999,3001],{"className":3000,"style":2938},[1887],[1788,3002,3003,3006],{"style":2941},[1788,3004],{"className":3005,"style":1895},[1894],[1788,3007,3009],{"className":3008},[1899,1900,1901,1902],[1788,3010,3012],{"className":3011},[1844,1902],[1788,3013,2896],{"className":3014},[1844,1902],[1788,3016,2958],{"className":3017},[2957],[1788,3019,3021],{"className":3020},[1883],[1788,3022,3024],{"className":3023,"style":2965},[1887],[1788,3025],{},[1788,3027],{"className":3028,"style":3029},[1850],"margin-right:0.2222em;",[1788,3031,2899],{"className":3032},[3033],"mbin",[1788,3035],{"className":3036,"style":3029},[1850],[1788,3038,3040,3043],{"className":3039},[1835],[1788,3041],{"className":3042,"style":2041},[1839],[1788,3044,3046,3049],{"className":3045},[1844],[1788,3047,2850],{"className":3048,"style":2866},[1844,1845],[1788,3050,3052],{"className":3051},[1875],[1788,3053,3055,3078],{"className":3054},[1879,2931],[1788,3056,3058,3075],{"className":3057},[1883],[1788,3059,3061],{"className":3060,"style":2938},[1887],[1788,3062,3063,3066],{"style":2941},[1788,3064],{"className":3065,"style":1895},[1894],[1788,3067,3069],{"className":3068},[1899,1900,1901,1902],[1788,3070,3072],{"className":3071},[1844,1902],[1788,3073,2906],{"className":3074},[1844,1902],[1788,3076,2958],{"className":3077},[2957],[1788,3079,3081],{"className":3080},[1883],[1788,3082,3084],{"className":3083,"style":2965},[1887],[1788,3085],{},"，",[1788,3088,3090,3105],{"className":3089},[1791],[1788,3091,3093],{"className":3092},[1795],[1797,3094,3095],{"xmlns":1799},[1801,3096,3097,3102],{},[1804,3098,3099],{},[1807,3100,3101],{},"α",[1823,3103,3104],{"encoding":1825},"\\alpha",[1788,3106,3108],{"className":3107,"ariaHidden":1831},[1830],[1788,3109,3111,3115],{"className":3110},[1835],[1788,3112],{"className":3113,"style":3114},[1839],"height:0.4306em;",[1788,3116,3101],{"className":3117,"style":3118},[1844,1845],"margin-right:0.0037em;"," 矩阵同样有这样的关系。",[1096,3121,3122],{},[2114,3123],{"alt":3124,"src":3125},"极大无关组","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be11d0e76.png",[1780,3127,3129],{"id":3128},"_6-求向量组的秩时行列变换都可","6. 求向量组的秩时，行列变换都可",[1096,3131,3132],{},"求向量组的秩，其实最后会转化为求矩阵的秩，原理就是**\"矩阵的秩＝行向量组的秩＝列向量组的秩\"**，所以求向量组的秩也是行列变换都可。",[1096,3134,3135],{},[2114,3136],{"alt":3137,"src":3138},"向量组的秩","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be12a3bfe.png",[1096,3140,3141],{},"但是一般求向量组的秩后面会继续求解极大无关组\u002F线性表出关系，这时只能做行变换，所以还是建议从开头就只使用行变换。",[1780,3143,3145],{"id":3144},"_7-求特征值时行列变换都可","7. 求特征值时，行列变换都可",[1096,3147,3148],{},"因为特征多项式本质上是行列式，求行列式时，行列都可以换。",[1096,3150,3151],{},[2114,3152],{"alt":3153,"src":3154},"求特征值","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be12cb40c.png",[1780,3156,3158],{"id":3157},"_8-求特征向量时仅做行变换","8. 求特征向量时，仅做行变换",[1096,3160,3161],{},"因为求特征向量时，本质是在解线性方程组，只能进行初等行变换。",[1096,3163,3164],{},[2114,3165],{"alt":3166,"src":3167},"求特征向量","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be12abf5d.png",[1780,3169,3171,3172,3226],{"id":3170},"_9-求逆矩阵时对-aeaeae-仅做初等行变换","9. 求逆矩阵时，对 ",[1788,3173,3175,3198],{"className":3174},[1791],[1788,3176,3178],{"className":3177},[1795],[1797,3179,3180],{"xmlns":1799},[1801,3181,3182,3195],{},[1804,3183,3184,3186,3188,3190,3193],{},[1811,3185,1977],{"stretchy":1976},[1807,3187,2290],{},[1811,3189,2430],{"separator":1831},[1807,3191,3192],{},"E",[1811,3194,1990],{"stretchy":1976},[1823,3196,3197],{"encoding":1825},"(A,E)",[1788,3199,3201],{"className":3200,"ariaHidden":1831},[1830],[1788,3202,3204,3207,3210,3213,3216,3219,3223],{"className":3203},[1835],[1788,3205],{"className":3206,"style":2003},[1839],[1788,3208,1977],{"className":3209},[2013],[1788,3211,2290],{"className":3212},[1844,1845],[1788,3214,2430],{"className":3215},[2474],[1788,3217],{"className":3218,"style":2478},[1850],[1788,3220,3192],{"className":3221,"style":3222},[1844,1845],"margin-right:0.0576em;",[1788,3224,1990],{"className":3225},[2079]," 仅做初等行变换",[1096,3228,3229,3230,3301,3302,3330,3331,3359,3360,3301,3428,3330,3456,3359,3524,3592],{},"因为以 ",[1788,3231,3233,3256],{"className":3232},[1791],[1788,3234,3236],{"className":3235},[1795],[1797,3237,3238],{"xmlns":1799},[1801,3239,3240,3253],{},[1804,3241,3242],{},[1815,3243,3244,3246],{},[1807,3245,2290],{},[1804,3247,3248,3251],{},[1811,3249,3250],{},"−",[1985,3252,2906],{},[1823,3254,3255],{"encoding":1825},"A^{-1}",[1788,3257,3259],{"className":3258,"ariaHidden":1831},[1830],[1788,3260,3262,3266],{"className":3261},[1835],[1788,3263],{"className":3264,"style":3265},[1839],"height:0.8141em;",[1788,3267,3269,3272],{"className":3268},[1844],[1788,3270,2290],{"className":3271},[1844,1845],[1788,3273,3275],{"className":3274},[1875],[1788,3276,3278],{"className":3277},[1879],[1788,3279,3281],{"className":3280},[1883],[1788,3282,3284],{"className":3283,"style":3265},[1887],[1788,3285,3286,3289],{"style":1890},[1788,3287],{"className":3288,"style":1895},[1894],[1788,3290,3292],{"className":3291},[1899,1900,1901,1902],[1788,3293,3295,3298],{"className":3294},[1844,1902],[1788,3296,3250],{"className":3297},[1844,1902],[1788,3299,2906],{"className":3300},[1844,1902]," 左乘 ",[1788,3303,3305,3318],{"className":3304},[1791],[1788,3306,3308],{"className":3307},[1795],[1797,3309,3310],{"xmlns":1799},[1801,3311,3312,3316],{},[1804,3313,3314],{},[1807,3315,2290],{},[1823,3317,2290],{"encoding":1825},[1788,3319,3321],{"className":3320,"ariaHidden":1831},[1830],[1788,3322,3324,3327],{"className":3323},[1835],[1788,3325],{"className":3326,"style":1840},[1839],[1788,3328,2290],{"className":3329},[1844,1845]," 得到 ",[1788,3332,3334,3347],{"className":3333},[1791],[1788,3335,3337],{"className":3336},[1795],[1797,3338,3339],{"xmlns":1799},[1801,3340,3341,3345],{},[1804,3342,3343],{},[1807,3344,3192],{},[1823,3346,3192],{"encoding":1825},[1788,3348,3350],{"className":3349,"ariaHidden":1831},[1830],[1788,3351,3353,3356],{"className":3352},[1835],[1788,3354],{"className":3355,"style":1840},[1839],[1788,3357,3192],{"className":3358,"style":3222},[1844,1845],"，以 ",[1788,3361,3363,3384],{"className":3362},[1791],[1788,3364,3366],{"className":3365},[1795],[1797,3367,3368],{"xmlns":1799},[1801,3369,3370,3382],{},[1804,3371,3372],{},[1815,3373,3374,3376],{},[1807,3375,2290],{},[1804,3377,3378,3380],{},[1811,3379,3250],{},[1985,3381,2906],{},[1823,3383,3255],{"encoding":1825},[1788,3385,3387],{"className":3386,"ariaHidden":1831},[1830],[1788,3388,3390,3393],{"className":3389},[1835],[1788,3391],{"className":3392,"style":3265},[1839],[1788,3394,3396,3399],{"className":3395},[1844],[1788,3397,2290],{"className":3398},[1844,1845],[1788,3400,3402],{"className":3401},[1875],[1788,3403,3405],{"className":3404},[1879],[1788,3406,3408],{"className":3407},[1883],[1788,3409,3411],{"className":3410,"style":3265},[1887],[1788,3412,3413,3416],{"style":1890},[1788,3414],{"className":3415,"style":1895},[1894],[1788,3417,3419],{"className":3418},[1899,1900,1901,1902],[1788,3420,3422,3425],{"className":3421},[1844,1902],[1788,3423,3250],{"className":3424},[1844,1902],[1788,3426,2906],{"className":3427},[1844,1902],[1788,3429,3431,3444],{"className":3430},[1791],[1788,3432,3434],{"className":3433},[1795],[1797,3435,3436],{"xmlns":1799},[1801,3437,3438,3442],{},[1804,3439,3440],{},[1807,3441,3192],{},[1823,3443,3192],{"encoding":1825},[1788,3445,3447],{"className":3446,"ariaHidden":1831},[1830],[1788,3448,3450,3453],{"className":3449},[1835],[1788,3451],{"className":3452,"style":1840},[1839],[1788,3454,3192],{"className":3455,"style":3222},[1844,1845],[1788,3457,3459,3480],{"className":3458},[1791],[1788,3460,3462],{"className":3461},[1795],[1797,3463,3464],{"xmlns":1799},[1801,3465,3466,3478],{},[1804,3467,3468],{},[1815,3469,3470,3472],{},[1807,3471,2290],{},[1804,3473,3474,3476],{},[1811,3475,3250],{},[1985,3477,2906],{},[1823,3479,3255],{"encoding":1825},[1788,3481,3483],{"className":3482,"ariaHidden":1831},[1830],[1788,3484,3486,3489],{"className":3485},[1835],[1788,3487],{"className":3488,"style":3265},[1839],[1788,3490,3492,3495],{"className":3491},[1844],[1788,3493,2290],{"className":3494},[1844,1845],[1788,3496,3498],{"className":3497},[1875],[1788,3499,3501],{"className":3500},[1879],[1788,3502,3504],{"className":3503},[1883],[1788,3505,3507],{"className":3506,"style":3265},[1887],[1788,3508,3509,3512],{"style":1890},[1788,3510],{"className":3511,"style":1895},[1894],[1788,3513,3515],{"className":3514},[1899,1900,1901,1902],[1788,3516,3518,3521],{"className":3517},[1844,1902],[1788,3519,3250],{"className":3520},[1844,1902],[1788,3522,2906],{"className":3523},[1844,1902],[1788,3525,3527,3548],{"className":3526},[1791],[1788,3528,3530],{"className":3529},[1795],[1797,3531,3532],{"xmlns":1799},[1801,3533,3534,3546],{},[1804,3535,3536],{},[1815,3537,3538,3540],{},[1807,3539,2290],{},[1804,3541,3542,3544],{},[1811,3543,3250],{},[1985,3545,2906],{},[1823,3547,3255],{"encoding":1825},[1788,3549,3551],{"className":3550,"ariaHidden":1831},[1830],[1788,3552,3554,3557],{"className":3553},[1835],[1788,3555],{"className":3556,"style":3265},[1839],[1788,3558,3560,3563],{"className":3559},[1844],[1788,3561,2290],{"className":3562},[1844,1845],[1788,3564,3566],{"className":3565},[1875],[1788,3567,3569],{"className":3568},[1879],[1788,3570,3572],{"className":3571},[1883],[1788,3573,3575],{"className":3574,"style":3265},[1887],[1788,3576,3577,3580],{"style":1890},[1788,3578],{"className":3579,"style":1895},[1894],[1788,3581,3583],{"className":3582},[1899,1900,1901,1902],[1788,3584,3586,3589],{"className":3585},[1844,1902],[1788,3587,3250],{"className":3588},[1844,1902],[1788,3590,2906],{"className":3591},[1844,1902]," 左乘的过程就是做初等行变换的过程。",[1096,3594,3595],{},[2114,3596],{"alt":3597,"src":3598},"求逆矩阵（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be136ee86.png",[1096,3600,3601,3602,3630,3631,3659,3660,3728,3729,3757,3758,3786],{},"所以怎么体现 ",[1788,3603,3605,3618],{"className":3604},[1791],[1788,3606,3608],{"className":3607},[1795],[1797,3609,3610],{"xmlns":1799},[1801,3611,3612,3616],{},[1804,3613,3614],{},[1807,3615,2290],{},[1823,3617,2290],{"encoding":1825},[1788,3619,3621],{"className":3620,"ariaHidden":1831},[1830],[1788,3622,3624,3627],{"className":3623},[1835],[1788,3625],{"className":3626,"style":1840},[1839],[1788,3628,2290],{"className":3629},[1844,1845]," 和 ",[1788,3632,3634,3647],{"className":3633},[1791],[1788,3635,3637],{"className":3636},[1795],[1797,3638,3639],{"xmlns":1799},[1801,3640,3641,3645],{},[1804,3642,3643],{},[1807,3644,3192],{},[1823,3646,3192],{"encoding":1825},[1788,3648,3650],{"className":3649,"ariaHidden":1831},[1830],[1788,3651,3653,3656],{"className":3652},[1835],[1788,3654],{"className":3655,"style":1840},[1839],[1788,3657,3192],{"className":3658,"style":3222},[1844,1845]," 做了完全一样的 ",[1788,3661,3663,3684],{"className":3662},[1791],[1788,3664,3666],{"className":3665},[1795],[1797,3667,3668],{"xmlns":1799},[1801,3669,3670,3682],{},[1804,3671,3672],{},[1815,3673,3674,3676],{},[1807,3675,2290],{},[1804,3677,3678,3680],{},[1811,3679,3250],{},[1985,3681,2906],{},[1823,3683,3255],{"encoding":1825},[1788,3685,3687],{"className":3686,"ariaHidden":1831},[1830],[1788,3688,3690,3693],{"className":3689},[1835],[1788,3691],{"className":3692,"style":3265},[1839],[1788,3694,3696,3699],{"className":3695},[1844],[1788,3697,2290],{"className":3698},[1844,1845],[1788,3700,3702],{"className":3701},[1875],[1788,3703,3705],{"className":3704},[1879],[1788,3706,3708],{"className":3707},[1883],[1788,3709,3711],{"className":3710,"style":3265},[1887],[1788,3712,3713,3716],{"style":1890},[1788,3714],{"className":3715,"style":1895},[1894],[1788,3717,3719],{"className":3718},[1899,1900,1901,1902],[1788,3720,3722,3725],{"className":3721},[1844,1902],[1788,3723,3250],{"className":3724},[1844,1902],[1788,3726,2906],{"className":3727},[1844,1902]," 所带来的初等行变换，就是将 ",[1788,3730,3732,3745],{"className":3731},[1791],[1788,3733,3735],{"className":3734},[1795],[1797,3736,3737],{"xmlns":1799},[1801,3738,3739,3743],{},[1804,3740,3741],{},[1807,3742,2290],{},[1823,3744,2290],{"encoding":1825},[1788,3746,3748],{"className":3747,"ariaHidden":1831},[1830],[1788,3749,3751,3754],{"className":3750},[1835],[1788,3752],{"className":3753,"style":1840},[1839],[1788,3755,2290],{"className":3756},[1844,1845],"、",[1788,3759,3761,3774],{"className":3760},[1791],[1788,3762,3764],{"className":3763},[1795],[1797,3765,3766],{"xmlns":1799},[1801,3767,3768,3772],{},[1804,3769,3770],{},[1807,3771,3192],{},[1823,3773,3192],{"encoding":1825},[1788,3775,3777],{"className":3776,"ariaHidden":1831},[1830],[1788,3778,3780,3783],{"className":3779},[1835],[1788,3781],{"className":3782,"style":1840},[1839],[1788,3784,3192],{"className":3785,"style":3222},[1844,1845]," 横着拼在一起，此时做的初等行变换就是同步的了。",[1096,3788,3789],{},[2114,3790],{"alt":3791,"src":3792},"求逆矩阵（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be13a4143.png",[1780,3794,2823],{"id":2823},[1912,3796,3797],{},[1096,3798,3799],{},"除了① 求行列式的值（求特征值本质上就是求行列式的值）和 ② 单纯求秩，行列变换都可，其余情况通通只做行变换。",[1091,3801,3803],{"id":3802},"二-要牢记","二. 要牢记",[1096,3805,3806],{},"先写那么多，后面有再补充：",[1096,3808,3809],{},[2114,3810],{"alt":3811,"src":3812},"要牢记","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be14cf11b.png",[1096,3814,3815],{},"一些推导：",[1096,3817,3818],{},[2114,3819],{"alt":3820,"src":3821},"推导（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be155866b.png",[1096,3823,3824,3825,3921],{},"对于 ",[1788,3826,3828,3851],{"className":3827},[1791],[1788,3829,3831],{"className":3830},[1795],[1797,3832,3833],{"xmlns":1799},[1801,3834,3835,3848],{},[1804,3836,3837,3839,3842,3844,3846],{},[1807,3838,2290],{},[1807,3840,3841],{},"B",[1811,3843,1983],{"mathvariant":1982},[1807,3845,3841],{},[1807,3847,2290],{},[1823,3849,3850],{"encoding":1825},"AB\\neq BA",[1788,3852,3854,3909],{"className":3853,"ariaHidden":1831},[1830],[1788,3855,3857,3860,3863,3867,3870,3906],{"className":3856},[1835],[1788,3858],{"className":3859,"style":2041},[1839],[1788,3861,2290],{"className":3862},[1844,1845],[1788,3864,3841],{"className":3865,"style":3866},[1844,1845],"margin-right:0.0502em;",[1788,3868],{"className":3869,"style":1851},[1850],[1788,3871,3873,3900,3903],{"className":3872},[1855],[1788,3874,3876],{"className":3875},[1855],[1788,3877,3879],{"className":3878},[1844,2029],[1788,3880,3882],{"className":3881},[2033],[1788,3883,3885,3888,3897],{"className":3884},[2037],[1788,3886],{"className":3887,"style":2041},[1839],[1788,3889,3891],{"className":3890},[2045],[1788,3892,3894],{"className":3893},[1844],[1788,3895,2052],{"className":3896},[1855],[1788,3898],{"className":3899},[2056],[1788,3901],{"className":3902},[1850,2060],[1788,3904,1813],{"className":3905},[1855],[1788,3907],{"className":3908,"style":1851},[1850],[1788,3910,3912,3915,3918],{"className":3911},[1835],[1788,3913],{"className":3914,"style":1840},[1839],[1788,3916,3841],{"className":3917,"style":3866},[1844,1845],[1788,3919,2290],{"className":3920},[1844,1845]," 的补充：",[1096,3923,3924],{},[2114,3925],{"alt":3926,"src":3927},"AB≠BA（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be15c5aa1.png",[1096,3929,3930],{},[2114,3931],{"alt":3932,"src":3933},"AB≠BA（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be14e0fc5.jpeg",[1780,3935,3937],{"id":3936},"_1-矩阵的逆","1. 矩阵的逆",[1096,3939,3940],{},[2114,3941],{"alt":3942,"src":3943},"矩阵的逆","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1690f49.png",[1096,3945,3946],{},"推导如下：",[1096,3948,3949],{},[2114,3950],{"alt":3951,"src":3952},"矩阵的逆推导","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be168227d.png",[1096,3954,3955],{},[1099,3956,3957],{},"初等矩阵的逆：",[1096,3959,3960],{},[2114,3961],{"alt":3962,"src":3963},"初等矩阵的逆","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be16ad19b.png",[1780,3965,3967],{"id":3966},"_2-矩阵的伴随","2. 矩阵的伴随",[1096,3969,3970],{},[2114,3971],{"alt":3972,"src":3973},"矩阵的伴随","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be16d31f9.png",[1091,3975,3977],{"id":3976},"三-某某子式","三. 某某子式",[1780,3979,3981],{"id":3980},"_1-余子式","1. 余子式",[1096,3983,3984,3985,4013,4014,4099,4100,4129,4130,4159,4160,4213,4214,4290,4291,2389],{},"在 ",[1788,3986,3988,4001],{"className":3987},[1791],[1788,3989,3991],{"className":3990},[1795],[1797,3992,3993],{"xmlns":1799},[1801,3994,3995,3999],{},[1804,3996,3997],{},[1807,3998,2301],{},[1823,4000,2301],{"encoding":1825},[1788,4002,4004],{"className":4003,"ariaHidden":1831},[1830],[1788,4005,4007,4010],{"className":4006},[1835],[1788,4008],{"className":4009,"style":3114},[1839],[1788,4011,2301],{"className":4012},[1844,1845]," 阶行列式中，去掉元素 ",[1788,4015,4017,4041],{"className":4016},[1791],[1788,4018,4020],{"className":4019},[1795],[1797,4021,4022],{"xmlns":1799},[1801,4023,4024,4038],{},[1804,4025,4026],{},[2881,4027,4028,4030],{},[1807,4029,1105],{},[1804,4031,4032,4035],{},[1807,4033,4034],{},"i",[1807,4036,4037],{},"j",[1823,4039,4040],{"encoding":1825},"a_{ij}",[1788,4042,4044],{"className":4043,"ariaHidden":1831},[1830],[1788,4045,4047,4051],{"className":4046},[1835],[1788,4048],{"className":4049,"style":4050},[1839],"height:0.7167em;vertical-align:-0.2861em;",[1788,4052,4054,4057],{"className":4053},[1844],[1788,4055,1105],{"className":4056},[1844,1845],[1788,4058,4060],{"className":4059},[1875],[1788,4061,4063,4090],{"className":4062},[1879,2931],[1788,4064,4066,4087],{"className":4065},[1883],[1788,4067,4070],{"className":4068,"style":4069},[1887],"height:0.3117em;",[1788,4071,4073,4076],{"style":4072},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1788,4074],{"className":4075,"style":1895},[1894],[1788,4077,4079],{"className":4078},[1899,1900,1901,1902],[1788,4080,4082],{"className":4081},[1844,1902],[1788,4083,4086],{"className":4084,"style":4085},[1844,1845,1902],"margin-right:0.0572em;","ij",[1788,4088,2958],{"className":4089},[2957],[1788,4091,4093],{"className":4092},[1883],[1788,4094,4097],{"className":4095,"style":4096},[1887],"height:0.2861em;",[1788,4098],{}," 所在的第 ",[1788,4101,4103,4116],{"className":4102},[1791],[1788,4104,4106],{"className":4105},[1795],[1797,4107,4108],{"xmlns":1799},[1801,4109,4110,4114],{},[1804,4111,4112],{},[1807,4113,4034],{},[1823,4115,4034],{"encoding":1825},[1788,4117,4119],{"className":4118,"ariaHidden":1831},[1830],[1788,4120,4122,4126],{"className":4121},[1835],[1788,4123],{"className":4124,"style":4125},[1839],"height:0.6595em;",[1788,4127,4034],{"className":4128},[1844,1845]," 行、第 ",[1788,4131,4133,4146],{"className":4132},[1791],[1788,4134,4136],{"className":4135},[1795],[1797,4137,4138],{"xmlns":1799},[1801,4139,4140,4144],{},[1804,4141,4142],{},[1807,4143,4037],{},[1823,4145,4037],{"encoding":1825},[1788,4147,4149],{"className":4148,"ariaHidden":1831},[1830],[1788,4150,4152,4156],{"className":4151},[1835],[1788,4153],{"className":4154,"style":4155},[1839],"height:0.854em;vertical-align:-0.1944em;",[1788,4157,4037],{"className":4158,"style":4085},[1844,1845]," 列元素，由剩下的元素按原来的位置与顺序组成的 ",[1788,4161,4163,4181],{"className":4162},[1791],[1788,4164,4166],{"className":4165},[1795],[1797,4167,4168],{"xmlns":1799},[1801,4169,4170,4178],{},[1804,4171,4172,4174,4176],{},[1807,4173,2301],{},[1811,4175,3250],{},[1985,4177,2906],{},[1823,4179,4180],{"encoding":1825},"n-1",[1788,4182,4184,4203],{"className":4183,"ariaHidden":1831},[1830],[1788,4185,4187,4191,4194,4197,4200],{"className":4186},[1835],[1788,4188],{"className":4189,"style":4190},[1839],"height:0.6667em;vertical-align:-0.0833em;",[1788,4192,2301],{"className":4193},[1844,1845],[1788,4195],{"className":4196,"style":3029},[1850],[1788,4198,3250],{"className":4199},[3033],[1788,4201],{"className":4202,"style":3029},[1850],[1788,4204,4206,4210],{"className":4205},[1835],[1788,4207],{"className":4208,"style":4209},[1839],"height:0.6444em;",[1788,4211,2906],{"className":4212},[1844]," 阶行列式称为元素 ",[1788,4215,4217,4238],{"className":4216},[1791],[1788,4218,4220],{"className":4219},[1795],[1797,4221,4222],{"xmlns":1799},[1801,4223,4224,4236],{},[1804,4225,4226],{},[2881,4227,4228,4230],{},[1807,4229,1105],{},[1804,4231,4232,4234],{},[1807,4233,4034],{},[1807,4235,4037],{},[1823,4237,4040],{"encoding":1825},[1788,4239,4241],{"className":4240,"ariaHidden":1831},[1830],[1788,4242,4244,4247],{"className":4243},[1835],[1788,4245],{"className":4246,"style":4050},[1839],[1788,4248,4250,4253],{"className":4249},[1844],[1788,4251,1105],{"className":4252},[1844,1845],[1788,4254,4256],{"className":4255},[1875],[1788,4257,4259,4282],{"className":4258},[1879,2931],[1788,4260,4262,4279],{"className":4261},[1883],[1788,4263,4265],{"className":4264,"style":4069},[1887],[1788,4266,4267,4270],{"style":4072},[1788,4268],{"className":4269,"style":1895},[1894],[1788,4271,4273],{"className":4272},[1899,1900,1901,1902],[1788,4274,4276],{"className":4275},[1844,1902],[1788,4277,4086],{"className":4278,"style":4085},[1844,1845,1902],[1788,4280,2958],{"className":4281},[2957],[1788,4283,4285],{"className":4284},[1883],[1788,4286,4288],{"className":4287,"style":4096},[1887],[1788,4289],{}," 的余子式，记作 ",[1788,4292,4294,4317],{"className":4293},[1791],[1788,4295,4297],{"className":4296},[1795],[1797,4298,4299],{"xmlns":1799},[1801,4300,4301,4314],{},[1804,4302,4303],{},[2881,4304,4305,4308],{},[1807,4306,4307],{},"M",[1804,4309,4310,4312],{},[1807,4311,4034],{},[1807,4313,4037],{},[1823,4315,4316],{"encoding":1825},"M_{ij}",[1788,4318,4320],{"className":4319,"ariaHidden":1831},[1830],[1788,4321,4323,4327],{"className":4322},[1835],[1788,4324],{"className":4325,"style":4326},[1839],"height:0.9694em;vertical-align:-0.2861em;",[1788,4328,4330,4334],{"className":4329},[1844],[1788,4331,4307],{"className":4332,"style":4333},[1844,1845],"margin-right:0.109em;",[1788,4335,4337],{"className":4336},[1875],[1788,4338,4340,4364],{"className":4339},[1879,2931],[1788,4341,4343,4361],{"className":4342},[1883],[1788,4344,4346],{"className":4345,"style":4069},[1887],[1788,4347,4349,4352],{"style":4348},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1788,4350],{"className":4351,"style":1895},[1894],[1788,4353,4355],{"className":4354},[1899,1900,1901,1902],[1788,4356,4358],{"className":4357},[1844,1902],[1788,4359,4086],{"className":4360,"style":4085},[1844,1845,1902],[1788,4362,2958],{"className":4363},[2957],[1788,4365,4367],{"className":4366},[1883],[1788,4368,4370],{"className":4369,"style":4096},[1887],[1788,4371],{},[1780,4373,4375],{"id":4374},"_2-代数余子式","2. 代数余子式",[1096,4377,4378,4379,4455,4456,4547,4548,4624,4625,2389],{},"余子式 ",[1788,4380,4382,4403],{"className":4381},[1791],[1788,4383,4385],{"className":4384},[1795],[1797,4386,4387],{"xmlns":1799},[1801,4388,4389,4401],{},[1804,4390,4391],{},[2881,4392,4393,4395],{},[1807,4394,4307],{},[1804,4396,4397,4399],{},[1807,4398,4034],{},[1807,4400,4037],{},[1823,4402,4316],{"encoding":1825},[1788,4404,4406],{"className":4405,"ariaHidden":1831},[1830],[1788,4407,4409,4412],{"className":4408},[1835],[1788,4410],{"className":4411,"style":4326},[1839],[1788,4413,4415,4418],{"className":4414},[1844],[1788,4416,4307],{"className":4417,"style":4333},[1844,1845],[1788,4419,4421],{"className":4420},[1875],[1788,4422,4424,4447],{"className":4423},[1879,2931],[1788,4425,4427,4444],{"className":4426},[1883],[1788,4428,4430],{"className":4429,"style":4069},[1887],[1788,4431,4432,4435],{"style":4348},[1788,4433],{"className":4434,"style":1895},[1894],[1788,4436,4438],{"className":4437},[1899,1900,1901,1902],[1788,4439,4441],{"className":4440},[1844,1902],[1788,4442,4086],{"className":4443,"style":4085},[1844,1845,1902],[1788,4445,2958],{"className":4446},[2957],[1788,4448,4450],{"className":4449},[1883],[1788,4451,4453],{"className":4452,"style":4096},[1887],[1788,4454],{}," 乘 ",[1788,4457,4459,4489],{"className":4458},[1791],[1788,4460,4462],{"className":4461},[1795],[1797,4463,4464],{"xmlns":1799},[1801,4465,4466,4486],{},[1804,4467,4468,4470,4472,4474],{},[1811,4469,1977],{"stretchy":1976},[1811,4471,3250],{},[1985,4473,2906],{},[1815,4475,4476,4478],{},[1811,4477,1990],{"stretchy":1976},[1804,4479,4480,4482,4484],{},[1807,4481,4034],{},[1811,4483,2899],{},[1807,4485,4037],{},[1823,4487,4488],{"encoding":1825},"(-1)^{i+j}",[1788,4490,4492],{"className":4491,"ariaHidden":1831},[1830],[1788,4493,4495,4499,4502,4505,4508],{"className":4494},[1835],[1788,4496],{"className":4497,"style":4498},[1839],"height:1.0747em;vertical-align:-0.25em;",[1788,4500,1977],{"className":4501},[2013],[1788,4503,3250],{"className":4504},[1844],[1788,4506,2906],{"className":4507},[1844],[1788,4509,4511,4514],{"className":4510},[2079],[1788,4512,1990],{"className":4513},[2079],[1788,4515,4517],{"className":4516},[1875],[1788,4518,4520],{"className":4519},[1879],[1788,4521,4523],{"className":4522},[1883],[1788,4524,4527],{"className":4525,"style":4526},[1887],"height:0.8247em;",[1788,4528,4529,4532],{"style":1890},[1788,4530],{"className":4531,"style":1895},[1894],[1788,4533,4535],{"className":4534},[1899,1900,1901,1902],[1788,4536,4538,4541,4544],{"className":4537},[1844,1902],[1788,4539,4034],{"className":4540},[1844,1845,1902],[1788,4542,2899],{"className":4543},[3033,1902],[1788,4545,4037],{"className":4546,"style":4085},[1844,1845,1902]," 后称为 ",[1788,4549,4551,4572],{"className":4550},[1791],[1788,4552,4554],{"className":4553},[1795],[1797,4555,4556],{"xmlns":1799},[1801,4557,4558,4570],{},[1804,4559,4560],{},[2881,4561,4562,4564],{},[1807,4563,1105],{},[1804,4565,4566,4568],{},[1807,4567,4034],{},[1807,4569,4037],{},[1823,4571,4040],{"encoding":1825},[1788,4573,4575],{"className":4574,"ariaHidden":1831},[1830],[1788,4576,4578,4581],{"className":4577},[1835],[1788,4579],{"className":4580,"style":4050},[1839],[1788,4582,4584,4587],{"className":4583},[1844],[1788,4585,1105],{"className":4586},[1844,1845],[1788,4588,4590],{"className":4589},[1875],[1788,4591,4593,4616],{"className":4592},[1879,2931],[1788,4594,4596,4613],{"className":4595},[1883],[1788,4597,4599],{"className":4598,"style":4069},[1887],[1788,4600,4601,4604],{"style":4072},[1788,4602],{"className":4603,"style":1895},[1894],[1788,4605,4607],{"className":4606},[1899,1900,1901,1902],[1788,4608,4610],{"className":4609},[1844,1902],[1788,4611,4086],{"className":4612,"style":4085},[1844,1845,1902],[1788,4614,2958],{"className":4615},[2957],[1788,4617,4619],{"className":4618},[1883],[1788,4620,4622],{"className":4621,"style":4096},[1887],[1788,4623],{}," 的代数余子式，记作 ",[1788,4626,4628,4650],{"className":4627},[1791],[1788,4629,4631],{"className":4630},[1795],[1797,4632,4633],{"xmlns":1799},[1801,4634,4635,4647],{},[1804,4636,4637],{},[2881,4638,4639,4641],{},[1807,4640,2290],{},[1804,4642,4643,4645],{},[1807,4644,4034],{},[1807,4646,4037],{},[1823,4648,4649],{"encoding":1825},"A_{ij}",[1788,4651,4653],{"className":4652,"ariaHidden":1831},[1830],[1788,4654,4656,4659],{"className":4655},[1835],[1788,4657],{"className":4658,"style":4326},[1839],[1788,4660,4662,4665],{"className":4661},[1844],[1788,4663,2290],{"className":4664},[1844,1845],[1788,4666,4668],{"className":4667},[1875],[1788,4669,4671,4694],{"className":4670},[1879,2931],[1788,4672,4674,4691],{"className":4673},[1883],[1788,4675,4677],{"className":4676,"style":4069},[1887],[1788,4678,4679,4682],{"style":4072},[1788,4680],{"className":4681,"style":1895},[1894],[1788,4683,4685],{"className":4684},[1899,1900,1901,1902],[1788,4686,4688],{"className":4687},[1844,1902],[1788,4689,4086],{"className":4690,"style":4085},[1844,1845,1902],[1788,4692,2958],{"className":4693},[2957],[1788,4695,4697],{"className":4696},[1883],[1788,4698,4700],{"className":4699,"style":4096},[1887],[1788,4701],{},[1096,4703,4704],{},[2114,4705],{"alt":4706,"src":4707},"代数余子式","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be177aa2f.png",[1780,4709,4711,4712,4740],{"id":4710},"_3-kkk-阶子式","3. ",[1788,4713,4715,4728],{"className":4714},[1791],[1788,4716,4718],{"className":4717},[1795],[1797,4719,4720],{"xmlns":1799},[1801,4721,4722,4726],{},[1804,4723,4724],{},[1807,4725,1938],{},[1823,4727,1938],{"encoding":1825},[1788,4729,4731],{"className":4730,"ariaHidden":1831},[1830],[1788,4732,4734,4737],{"className":4733},[1835],[1788,4735],{"className":4736,"style":1950},[1839],[1788,4738,1938],{"className":4739,"style":1954},[1844,1845]," 阶子式",[1096,4742,4743,4744,4772,4773,4801,4802,4864],{},"给定一个矩阵，任取 ",[1788,4745,4747,4760],{"className":4746},[1791],[1788,4748,4750],{"className":4749},[1795],[1797,4751,4752],{"xmlns":1799},[1801,4753,4754,4758],{},[1804,4755,4756],{},[1807,4757,1938],{},[1823,4759,1938],{"encoding":1825},[1788,4761,4763],{"className":4762,"ariaHidden":1831},[1830],[1788,4764,4766,4769],{"className":4765},[1835],[1788,4767],{"className":4768,"style":1950},[1839],[1788,4770,1938],{"className":4771,"style":1954},[1844,1845]," 行、任取 ",[1788,4774,4776,4789],{"className":4775},[1791],[1788,4777,4779],{"className":4778},[1795],[1797,4780,4781],{"xmlns":1799},[1801,4782,4783,4787],{},[1804,4784,4785],{},[1807,4786,1938],{},[1823,4788,1938],{"encoding":1825},[1788,4790,4792],{"className":4791,"ariaHidden":1831},[1830],[1788,4793,4795,4798],{"className":4794},[1835],[1788,4796],{"className":4797,"style":1950},[1839],[1788,4799,1938],{"className":4800,"style":1954},[1844,1845]," 列，共 ",[1788,4803,4805,4823],{"className":4804},[1791],[1788,4806,4808],{"className":4807},[1795],[1797,4809,4810],{"xmlns":1799},[1801,4811,4812,4820],{},[1804,4813,4814],{},[1815,4815,4816,4818],{},[1807,4817,1938],{},[1985,4819,2896],{},[1823,4821,4822],{"encoding":1825},"k^{2}",[1788,4824,4826],{"className":4825,"ariaHidden":1831},[1830],[1788,4827,4829,4832],{"className":4828},[1835],[1788,4830],{"className":4831,"style":3265},[1839],[1788,4833,4835,4838],{"className":4834},[1844],[1788,4836,1938],{"className":4837,"style":1954},[1844,1845],[1788,4839,4841],{"className":4840},[1875],[1788,4842,4844],{"className":4843},[1879],[1788,4845,4847],{"className":4846},[1883],[1788,4848,4850],{"className":4849,"style":3265},[1887],[1788,4851,4852,4855],{"style":1890},[1788,4853],{"className":4854,"style":1895},[1894],[1788,4856,4858],{"className":4857},[1899,1900,1901,1902],[1788,4859,4861],{"className":4860},[1844,1902],[1788,4862,2896],{"className":4863},[1844,1902]," 个数构成的行列式，出现在矩阵的秩中，定义如下：",[1096,4866,4867,4868,4896,4897,4950,4951,4979,4980,5008,5009,5061,5062,5128,5129,5157,5158,5209],{},"设 ",[1788,4869,4871,4884],{"className":4870},[1791],[1788,4872,4874],{"className":4873},[1795],[1797,4875,4876],{"xmlns":1799},[1801,4877,4878,4882],{},[1804,4879,4880],{},[1807,4881,2290],{},[1823,4883,2290],{"encoding":1825},[1788,4885,4887],{"className":4886,"ariaHidden":1831},[1830],[1788,4888,4890,4893],{"className":4889},[1835],[1788,4891],{"className":4892,"style":1840},[1839],[1788,4894,2290],{"className":4895},[1844,1845]," 是 ",[1788,4898,4900,4920],{"className":4899},[1791],[1788,4901,4903],{"className":4902},[1795],[1797,4904,4905],{"xmlns":1799},[1801,4906,4907,4917],{},[1804,4908,4909,4912,4915],{},[1807,4910,4911],{},"m",[1811,4913,4914],{},"×",[1807,4916,2301],{},[1823,4918,4919],{"encoding":1825},"m\\times n",[1788,4921,4923,4941],{"className":4922,"ariaHidden":1831},[1830],[1788,4924,4926,4929,4932,4935,4938],{"className":4925},[1835],[1788,4927],{"className":4928,"style":4190},[1839],[1788,4930,4911],{"className":4931},[1844,1845],[1788,4933],{"className":4934,"style":3029},[1850],[1788,4936,4914],{"className":4937},[3033],[1788,4939],{"className":4940,"style":3029},[1850],[1788,4942,4944,4947],{"className":4943},[1835],[1788,4945],{"className":4946,"style":3114},[1839],[1788,4948,2301],{"className":4949},[1844,1845]," 矩阵，若 ",[1788,4952,4954,4967],{"className":4953},[1791],[1788,4955,4957],{"className":4956},[1795],[1797,4958,4959],{"xmlns":1799},[1801,4960,4961,4965],{},[1804,4962,4963],{},[1807,4964,2290],{},[1823,4966,2290],{"encoding":1825},[1788,4968,4970],{"className":4969,"ariaHidden":1831},[1830],[1788,4971,4973,4976],{"className":4972},[1835],[1788,4974],{"className":4975,"style":1840},[1839],[1788,4977,2290],{"className":4978},[1844,1845]," 存在 ",[1788,4981,4983,4996],{"className":4982},[1791],[1788,4984,4986],{"className":4985},[1795],[1797,4987,4988],{"xmlns":1799},[1801,4989,4990,4994],{},[1804,4991,4992],{},[1807,4993,1938],{},[1823,4995,1938],{"encoding":1825},[1788,4997,4999],{"className":4998,"ariaHidden":1831},[1830],[1788,5000,5002,5005],{"className":5001},[1835],[1788,5003],{"className":5004,"style":1950},[1839],[1788,5006,1938],{"className":5007,"style":1954},[1844,1845]," 阶子式不为零，而任意 ",[1788,5010,5012,5030],{"className":5011},[1791],[1788,5013,5015],{"className":5014},[1795],[1797,5016,5017],{"xmlns":1799},[1801,5018,5019,5027],{},[1804,5020,5021,5023,5025],{},[1807,5022,1938],{},[1811,5024,2899],{},[1985,5026,2906],{},[1823,5028,5029],{"encoding":1825},"k+1",[1788,5031,5033,5052],{"className":5032,"ariaHidden":1831},[1830],[1788,5034,5036,5040,5043,5046,5049],{"className":5035},[1835],[1788,5037],{"className":5038,"style":5039},[1839],"height:0.7778em;vertical-align:-0.0833em;",[1788,5041,1938],{"className":5042,"style":1954},[1844,1845],[1788,5044],{"className":5045,"style":3029},[1850],[1788,5047,2899],{"className":5048},[3033],[1788,5050],{"className":5051,"style":3029},[1850],[1788,5053,5055,5058],{"className":5054},[1835],[1788,5056],{"className":5057,"style":4209},[1839],[1788,5059,2906],{"className":5060},[1844]," 阶子式（如果有的话）全为零，则 ",[1788,5063,5065,5089],{"className":5064},[1791],[1788,5066,5068],{"className":5067},[1795],[1797,5069,5070],{"xmlns":1799},[1801,5071,5072,5086],{},[1804,5073,5074,5076,5078,5080,5082,5084],{},[1807,5075,2421],{},[1811,5077,1977],{"stretchy":1976},[1807,5079,2290],{},[1811,5081,1990],{"stretchy":1976},[1811,5083,1813],{},[1807,5085,1938],{},[1823,5087,5088],{"encoding":1825},"r(A)=k",[1788,5090,5092,5119],{"className":5091,"ariaHidden":1831},[1830],[1788,5093,5095,5098,5101,5104,5107,5110,5113,5116],{"className":5094},[1835],[1788,5096],{"className":5097,"style":2003},[1839],[1788,5099,2421],{"className":5100,"style":1846},[1844,1845],[1788,5102,1977],{"className":5103},[2013],[1788,5105,2290],{"className":5106},[1844,1845],[1788,5108,1990],{"className":5109},[2079],[1788,5111],{"className":5112,"style":1851},[1850],[1788,5114,1813],{"className":5115},[1855],[1788,5117],{"className":5118,"style":1851},[1850],[1788,5120,5122,5125],{"className":5121},[1835],[1788,5123],{"className":5124,"style":1950},[1839],[1788,5126,1938],{"className":5127,"style":1954},[1844,1845],"。且若 ",[1788,5130,5132,5145],{"className":5131},[1791],[1788,5133,5135],{"className":5134},[1795],[1797,5136,5137],{"xmlns":1799},[1801,5138,5139,5143],{},[1804,5140,5141],{},[1807,5142,2290],{},[1823,5144,2290],{"encoding":1825},[1788,5146,5148],{"className":5147,"ariaHidden":1831},[1830],[1788,5149,5151,5154],{"className":5150},[1835],[1788,5152],{"className":5153,"style":1840},[1839],[1788,5155,2290],{"className":5156},[1844,1845]," 为 ",[1788,5159,5161,5179],{"className":5160},[1791],[1788,5162,5164],{"className":5163},[1795],[1797,5165,5166],{"xmlns":1799},[1801,5167,5168,5176],{},[1804,5169,5170,5172,5174],{},[1807,5171,2301],{},[1811,5173,4914],{},[1807,5175,2301],{},[1823,5177,5178],{"encoding":1825},"n\\times n",[1788,5180,5182,5200],{"className":5181,"ariaHidden":1831},[1830],[1788,5183,5185,5188,5191,5194,5197],{"className":5184},[1835],[1788,5186],{"className":5187,"style":4190},[1839],[1788,5189,2301],{"className":5190},[1844,1845],[1788,5192],{"className":5193,"style":3029},[1850],[1788,5195,4914],{"className":5196},[3033],[1788,5198],{"className":5199,"style":3029},[1850],[1788,5201,5203,5206],{"className":5202},[1835],[1788,5204],{"className":5205,"style":3114},[1839],[1788,5207,2301],{"className":5208},[1844,1845]," 矩阵，则",[1096,5211,5212],{},[2114,5213],{"alt":5214,"src":5215},"k阶子式","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be17bac82.png",[1780,5217,5219,5220,5248],{"id":5218},"_4-kkk-阶主子式","4. ",[1788,5221,5223,5236],{"className":5222},[1791],[1788,5224,5226],{"className":5225},[1795],[1797,5227,5228],{"xmlns":1799},[1801,5229,5230,5234],{},[1804,5231,5232],{},[1807,5233,1938],{},[1823,5235,1938],{"encoding":1825},[1788,5237,5239],{"className":5238,"ariaHidden":1831},[1830],[1788,5240,5242,5245],{"className":5241},[1835],[1788,5243],{"className":5244,"style":1950},[1839],[1788,5246,1938],{"className":5247,"style":1954},[1844,1845]," 阶主子式",[1096,5250,5251,5252,5280,5281,5309,5310,5490,5491,5670,5671,5490,5850,6028,6029,6057],{},"指在行列式中选 ",[1788,5253,5255,5268],{"className":5254},[1791],[1788,5256,5258],{"className":5257},[1795],[1797,5259,5260],{"xmlns":1799},[1801,5261,5262,5266],{},[1804,5263,5264],{},[1807,5265,1938],{},[1823,5267,1938],{"encoding":1825},[1788,5269,5271],{"className":5270,"ariaHidden":1831},[1830],[1788,5272,5274,5277],{"className":5273},[1835],[1788,5275],{"className":5276,"style":1950},[1839],[1788,5278,1938],{"className":5279,"style":1954},[1844,1845]," 行 ",[1788,5282,5284,5297],{"className":5283},[1791],[1788,5285,5287],{"className":5286},[1795],[1797,5288,5289],{"xmlns":1799},[1801,5290,5291,5295],{},[1804,5292,5293],{},[1807,5294,1938],{},[1823,5296,1938],{"encoding":1825},[1788,5298,5300],{"className":5299,"ariaHidden":1831},[1830],[1788,5301,5303,5306],{"className":5302},[1835],[1788,5304],{"className":5305,"style":1950},[1839],[1788,5307,1938],{"className":5308,"style":1954},[1844,1845]," 列，但要求行和列的下标相同。如：行为 ",[1788,5311,5313,5347],{"className":5312},[1791],[1788,5314,5316],{"className":5315},[1795],[1797,5317,5318],{"xmlns":1799},[1801,5319,5320,5344],{},[1804,5321,5322,5328,5330,5336,5338],{},[2881,5323,5324,5326],{},[1807,5325,2421],{},[1985,5327,2906],{},[1811,5329,2430],{"separator":1831},[2881,5331,5332,5334],{},[1807,5333,2421],{},[1985,5335,2896],{},[1811,5337,2430],{"separator":1831},[2881,5339,5340,5342],{},[1807,5341,2421],{},[1985,5343,2887],{},[1823,5345,5346],{"encoding":1825},"r_1,r_2,r_3",[1788,5348,5350],{"className":5349,"ariaHidden":1831},[1830],[1788,5351,5353,5357,5398,5401,5404,5444,5447,5450],{"className":5352},[1835],[1788,5354],{"className":5355,"style":5356},[1839],"height:0.625em;vertical-align:-0.1944em;",[1788,5358,5360,5363],{"className":5359},[1844],[1788,5361,2421],{"className":5362,"style":1846},[1844,1845],[1788,5364,5366],{"className":5365},[1875],[1788,5367,5369,5390],{"className":5368},[1879,2931],[1788,5370,5372,5387],{"className":5371},[1883],[1788,5373,5375],{"className":5374,"style":2938},[1887],[1788,5376,5378,5381],{"style":5377},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1788,5379],{"className":5380,"style":1895},[1894],[1788,5382,5384],{"className":5383},[1899,1900,1901,1902],[1788,5385,2906],{"className":5386},[1844,1902],[1788,5388,2958],{"className":5389},[2957],[1788,5391,5393],{"className":5392},[1883],[1788,5394,5396],{"className":5395,"style":2965},[1887],[1788,5397],{},[1788,5399,2430],{"className":5400},[2474],[1788,5402],{"className":5403,"style":2478},[1850],[1788,5405,5407,5410],{"className":5406},[1844],[1788,5408,2421],{"className":5409,"style":1846},[1844,1845],[1788,5411,5413],{"className":5412},[1875],[1788,5414,5416,5436],{"className":5415},[1879,2931],[1788,5417,5419,5433],{"className":5418},[1883],[1788,5420,5422],{"className":5421,"style":2938},[1887],[1788,5423,5424,5427],{"style":5377},[1788,5425],{"className":5426,"style":1895},[1894],[1788,5428,5430],{"className":5429},[1899,1900,1901,1902],[1788,5431,2896],{"className":5432},[1844,1902],[1788,5434,2958],{"className":5435},[2957],[1788,5437,5439],{"className":5438},[1883],[1788,5440,5442],{"className":5441,"style":2965},[1887],[1788,5443],{},[1788,5445,2430],{"className":5446},[2474],[1788,5448],{"className":5449,"style":2478},[1850],[1788,5451,5453,5456],{"className":5452},[1844],[1788,5454,2421],{"className":5455,"style":1846},[1844,1845],[1788,5457,5459],{"className":5458},[1875],[1788,5460,5462,5482],{"className":5461},[1879,2931],[1788,5463,5465,5479],{"className":5464},[1883],[1788,5466,5468],{"className":5467,"style":2938},[1887],[1788,5469,5470,5473],{"style":5377},[1788,5471],{"className":5472,"style":1895},[1894],[1788,5474,5476],{"className":5475},[1899,1900,1901,1902],[1788,5477,2887],{"className":5478},[1844,1902],[1788,5480,2958],{"className":5481},[2957],[1788,5483,5485],{"className":5484},[1883],[1788,5486,5488],{"className":5487,"style":2965},[1887],[1788,5489],{},"，列必须为 ",[1788,5492,5494,5529],{"className":5493},[1791],[1788,5495,5497],{"className":5496},[1795],[1797,5498,5499],{"xmlns":1799},[1801,5500,5501,5526],{},[1804,5502,5503,5510,5512,5518,5520],{},[2881,5504,5505,5508],{},[1807,5506,5507],{},"c",[1985,5509,2906],{},[1811,5511,2430],{"separator":1831},[2881,5513,5514,5516],{},[1807,5515,5507],{},[1985,5517,2896],{},[1811,5519,2430],{"separator":1831},[2881,5521,5522,5524],{},[1807,5523,5507],{},[1985,5525,2887],{},[1823,5527,5528],{"encoding":1825},"c_1,c_2,c_3",[1788,5530,5532],{"className":5531,"ariaHidden":1831},[1830],[1788,5533,5535,5538,5578,5581,5584,5624,5627,5630],{"className":5534},[1835],[1788,5536],{"className":5537,"style":5356},[1839],[1788,5539,5541,5544],{"className":5540},[1844],[1788,5542,5507],{"className":5543},[1844,1845],[1788,5545,5547],{"className":5546},[1875],[1788,5548,5550,5570],{"className":5549},[1879,2931],[1788,5551,5553,5567],{"className":5552},[1883],[1788,5554,5556],{"className":5555,"style":2938},[1887],[1788,5557,5558,5561],{"style":4072},[1788,5559],{"className":5560,"style":1895},[1894],[1788,5562,5564],{"className":5563},[1899,1900,1901,1902],[1788,5565,2906],{"className":5566},[1844,1902],[1788,5568,2958],{"className":5569},[2957],[1788,5571,5573],{"className":5572},[1883],[1788,5574,5576],{"className":5575,"style":2965},[1887],[1788,5577],{},[1788,5579,2430],{"className":5580},[2474],[1788,5582],{"className":5583,"style":2478},[1850],[1788,5585,5587,5590],{"className":5586},[1844],[1788,5588,5507],{"className":5589},[1844,1845],[1788,5591,5593],{"className":5592},[1875],[1788,5594,5596,5616],{"className":5595},[1879,2931],[1788,5597,5599,5613],{"className":5598},[1883],[1788,5600,5602],{"className":5601,"style":2938},[1887],[1788,5603,5604,5607],{"style":4072},[1788,5605],{"className":5606,"style":1895},[1894],[1788,5608,5610],{"className":5609},[1899,1900,1901,1902],[1788,5611,2896],{"className":5612},[1844,1902],[1788,5614,2958],{"className":5615},[2957],[1788,5617,5619],{"className":5618},[1883],[1788,5620,5622],{"className":5621,"style":2965},[1887],[1788,5623],{},[1788,5625,2430],{"className":5626},[2474],[1788,5628],{"className":5629,"style":2478},[1850],[1788,5631,5633,5636],{"className":5632},[1844],[1788,5634,5507],{"className":5635},[1844,1845],[1788,5637,5639],{"className":5638},[1875],[1788,5640,5642,5662],{"className":5641},[1879,2931],[1788,5643,5645,5659],{"className":5644},[1883],[1788,5646,5648],{"className":5647,"style":2938},[1887],[1788,5649,5650,5653],{"style":4072},[1788,5651],{"className":5652,"style":1895},[1894],[1788,5654,5656],{"className":5655},[1899,1900,1901,1902],[1788,5657,2887],{"className":5658},[1844,1902],[1788,5660,2958],{"className":5661},[2957],[1788,5663,5665],{"className":5664},[1883],[1788,5666,5668],{"className":5667,"style":2965},[1887],[1788,5669],{},"；行为 ",[1788,5672,5674,5709],{"className":5673},[1791],[1788,5675,5677],{"className":5676},[1795],[1797,5678,5679],{"xmlns":1799},[1801,5680,5681,5706],{},[1804,5682,5683,5689,5691,5697,5699],{},[2881,5684,5685,5687],{},[1807,5686,2421],{},[1985,5688,2896],{},[1811,5690,2430],{"separator":1831},[2881,5692,5693,5695],{},[1807,5694,2421],{},[1985,5696,2887],{},[1811,5698,2430],{"separator":1831},[2881,5700,5701,5703],{},[1807,5702,2421],{},[1985,5704,5705],{},"5",[1823,5707,5708],{"encoding":1825},"r_2,r_3,r_5",[1788,5710,5712],{"className":5711,"ariaHidden":1831},[1830],[1788,5713,5715,5718,5758,5761,5764,5804,5807,5810],{"className":5714},[1835],[1788,5716],{"className":5717,"style":5356},[1839],[1788,5719,5721,5724],{"className":5720},[1844],[1788,5722,2421],{"className":5723,"style":1846},[1844,1845],[1788,5725,5727],{"className":5726},[1875],[1788,5728,5730,5750],{"className":5729},[1879,2931],[1788,5731,5733,5747],{"className":5732},[1883],[1788,5734,5736],{"className":5735,"style":2938},[1887],[1788,5737,5738,5741],{"style":5377},[1788,5739],{"className":5740,"style":1895},[1894],[1788,5742,5744],{"className":5743},[1899,1900,1901,1902],[1788,5745,2896],{"className":5746},[1844,1902],[1788,5748,2958],{"className":5749},[2957],[1788,5751,5753],{"className":5752},[1883],[1788,5754,5756],{"className":5755,"style":2965},[1887],[1788,5757],{},[1788,5759,2430],{"className":5760},[2474],[1788,5762],{"className":5763,"style":2478},[1850],[1788,5765,5767,5770],{"className":5766},[1844],[1788,5768,2421],{"className":5769,"style":1846},[1844,1845],[1788,5771,5773],{"className":5772},[1875],[1788,5774,5776,5796],{"className":5775},[1879,2931],[1788,5777,5779,5793],{"className":5778},[1883],[1788,5780,5782],{"className":5781,"style":2938},[1887],[1788,5783,5784,5787],{"style":5377},[1788,5785],{"className":5786,"style":1895},[1894],[1788,5788,5790],{"className":5789},[1899,1900,1901,1902],[1788,5791,2887],{"className":5792},[1844,1902],[1788,5794,2958],{"className":5795},[2957],[1788,5797,5799],{"className":5798},[1883],[1788,5800,5802],{"className":5801,"style":2965},[1887],[1788,5803],{},[1788,5805,2430],{"className":5806},[2474],[1788,5808],{"className":5809,"style":2478},[1850],[1788,5811,5813,5816],{"className":5812},[1844],[1788,5814,2421],{"className":5815,"style":1846},[1844,1845],[1788,5817,5819],{"className":5818},[1875],[1788,5820,5822,5842],{"className":5821},[1879,2931],[1788,5823,5825,5839],{"className":5824},[1883],[1788,5826,5828],{"className":5827,"style":2938},[1887],[1788,5829,5830,5833],{"style":5377},[1788,5831],{"className":5832,"style":1895},[1894],[1788,5834,5836],{"className":5835},[1899,1900,1901,1902],[1788,5837,5705],{"className":5838},[1844,1902],[1788,5840,2958],{"className":5841},[2957],[1788,5843,5845],{"className":5844},[1883],[1788,5846,5848],{"className":5847,"style":2965},[1887],[1788,5849],{},[1788,5851,5853,5887],{"className":5852},[1791],[1788,5854,5856],{"className":5855},[1795],[1797,5857,5858],{"xmlns":1799},[1801,5859,5860,5884],{},[1804,5861,5862,5868,5870,5876,5878],{},[2881,5863,5864,5866],{},[1807,5865,5507],{},[1985,5867,2896],{},[1811,5869,2430],{"separator":1831},[2881,5871,5872,5874],{},[1807,5873,5507],{},[1985,5875,2887],{},[1811,5877,2430],{"separator":1831},[2881,5879,5880,5882],{},[1807,5881,5507],{},[1985,5883,5705],{},[1823,5885,5886],{"encoding":1825},"c_2,c_3,c_5",[1788,5888,5890],{"className":5889,"ariaHidden":1831},[1830],[1788,5891,5893,5896,5936,5939,5942,5982,5985,5988],{"className":5892},[1835],[1788,5894],{"className":5895,"style":5356},[1839],[1788,5897,5899,5902],{"className":5898},[1844],[1788,5900,5507],{"className":5901},[1844,1845],[1788,5903,5905],{"className":5904},[1875],[1788,5906,5908,5928],{"className":5907},[1879,2931],[1788,5909,5911,5925],{"className":5910},[1883],[1788,5912,5914],{"className":5913,"style":2938},[1887],[1788,5915,5916,5919],{"style":4072},[1788,5917],{"className":5918,"style":1895},[1894],[1788,5920,5922],{"className":5921},[1899,1900,1901,1902],[1788,5923,2896],{"className":5924},[1844,1902],[1788,5926,2958],{"className":5927},[2957],[1788,5929,5931],{"className":5930},[1883],[1788,5932,5934],{"className":5933,"style":2965},[1887],[1788,5935],{},[1788,5937,2430],{"className":5938},[2474],[1788,5940],{"className":5941,"style":2478},[1850],[1788,5943,5945,5948],{"className":5944},[1844],[1788,5946,5507],{"className":5947},[1844,1845],[1788,5949,5951],{"className":5950},[1875],[1788,5952,5954,5974],{"className":5953},[1879,2931],[1788,5955,5957,5971],{"className":5956},[1883],[1788,5958,5960],{"className":5959,"style":2938},[1887],[1788,5961,5962,5965],{"style":4072},[1788,5963],{"className":5964,"style":1895},[1894],[1788,5966,5968],{"className":5967},[1899,1900,1901,1902],[1788,5969,2887],{"className":5970},[1844,1902],[1788,5972,2958],{"className":5973},[2957],[1788,5975,5977],{"className":5976},[1883],[1788,5978,5980],{"className":5979,"style":2965},[1887],[1788,5981],{},[1788,5983,2430],{"className":5984},[2474],[1788,5986],{"className":5987,"style":2478},[1850],[1788,5989,5991,5994],{"className":5990},[1844],[1788,5992,5507],{"className":5993},[1844,1845],[1788,5995,5997],{"className":5996},[1875],[1788,5998,6000,6020],{"className":5999},[1879,2931],[1788,6001,6003,6017],{"className":6002},[1883],[1788,6004,6006],{"className":6005,"style":2938},[1887],[1788,6007,6008,6011],{"style":4072},[1788,6009],{"className":6010,"style":1895},[1894],[1788,6012,6014],{"className":6013},[1899,1900,1901,1902],[1788,6015,5705],{"className":6016},[1844,1902],[1788,6018,2958],{"className":6019},[2957],[1788,6021,6023],{"className":6022},[1883],[1788,6024,6026],{"className":6025,"style":2965},[1887],[1788,6027],{},"。因此，",[1788,6030,6032,6045],{"className":6031},[1791],[1788,6033,6035],{"className":6034},[1795],[1797,6036,6037],{"xmlns":1799},[1801,6038,6039,6043],{},[1804,6040,6041],{},[1807,6042,1938],{},[1823,6044,1938],{"encoding":1825},[1788,6046,6048],{"className":6047,"ariaHidden":1831},[1830],[1788,6049,6051,6054],{"className":6050},[1835],[1788,6052],{"className":6053,"style":1950},[1839],[1788,6055,1938],{"className":6056,"style":1954},[1844,1845]," 阶主子式不唯一。这在矩阵相似会用到，下面会讲。",[1780,6059,6061],{"id":6060},"_5-顺序主子式","5. 顺序主子式",[1096,6063,6064,6065,6117,6118,6168],{},"顺序主子式是在主子式上再加限定，顺序主子式是由 ",[1788,6066,6068,6087],{"className":6067},[1791],[1788,6069,6071],{"className":6070},[1795],[1797,6072,6073],{"xmlns":1799},[1801,6074,6075,6084],{},[1804,6076,6077,6079,6082],{},[1985,6078,2906],{},[1811,6080,6081],{},"∼",[1807,6083,1938],{},[1823,6085,6086],{"encoding":1825},"1\\sim k",[1788,6088,6090,6108],{"className":6089,"ariaHidden":1831},[1830],[1788,6091,6093,6096,6099,6102,6105],{"className":6092},[1835],[1788,6094],{"className":6095,"style":4209},[1839],[1788,6097,2906],{"className":6098},[1844],[1788,6100],{"className":6101,"style":1851},[1850],[1788,6103,6081],{"className":6104},[1855],[1788,6106],{"className":6107,"style":1851},[1850],[1788,6109,6111,6114],{"className":6110},[1835],[1788,6112],{"className":6113,"style":1950},[1839],[1788,6115,1938],{"className":6116,"style":1954},[1844,1845]," 行和 ",[1788,6119,6121,6138],{"className":6120},[1791],[1788,6122,6124],{"className":6123},[1795],[1797,6125,6126],{"xmlns":1799},[1801,6127,6128,6136],{},[1804,6129,6130,6132,6134],{},[1985,6131,2906],{},[1811,6133,6081],{},[1807,6135,1938],{},[1823,6137,6086],{"encoding":1825},[1788,6139,6141,6159],{"className":6140,"ariaHidden":1831},[1830],[1788,6142,6144,6147,6150,6153,6156],{"className":6143},[1835],[1788,6145],{"className":6146,"style":4209},[1839],[1788,6148,2906],{"className":6149},[1844],[1788,6151],{"className":6152,"style":1851},[1850],[1788,6154,6081],{"className":6155},[1855],[1788,6157],{"className":6158,"style":1851},[1850],[1788,6160,6162,6165],{"className":6161},[1835],[1788,6163],{"className":6164,"style":1950},[1839],[1788,6166,1938],{"className":6167,"style":1954},[1844,1845]," 列所确定的子式。",[1912,6170,6171,6176,6191],{},[1096,6172,6173],{},[1099,6174,6175],{},"例如：",[6177,6178,6179,6182,6185,6188],"ul",{},[1921,6180,6181],{},"1 阶时：取第 1 行，第 1 列",[1921,6183,6184],{},"2 阶时：取第 1、2 行，第 1、2 列",[1921,6186,6187],{},"3 阶时：取第 1、2、3 行，第 1、2、3 列",[1921,6189,6190],{},"4 阶时：取第 1、2、3、4 行，第 1、2、3、4 列",[1096,6192,6193,6194,6222,6223],{},"实际上，主子式的主对角线元素是原 ",[1788,6195,6197,6210],{"className":6196},[1791],[1788,6198,6200],{"className":6199},[1795],[1797,6201,6202],{"xmlns":1799},[1801,6203,6204,6208],{},[1804,6205,6206],{},[1807,6207,2301],{},[1823,6209,2301],{"encoding":1825},[1788,6211,6213],{"className":6212,"ariaHidden":1831},[1830],[1788,6214,6216,6219],{"className":6215},[1835],[1788,6217],{"className":6218,"style":3114},[1839],[1788,6220,2301],{"className":6221},[1844,1845]," 阶行列式的主对角线元素的一部分，",[1099,6224,6225],{},"且顺序相同。",[1096,6227,6228,6229,6257,6258,6289,6290,6293],{},"所以 ",[1788,6230,6232,6245],{"className":6231},[1791],[1788,6233,6235],{"className":6234},[1795],[1797,6236,6237],{"xmlns":1799},[1801,6238,6239,6243],{},[1804,6240,6241],{},[1807,6242,1938],{},[1823,6244,1938],{"encoding":1825},[1788,6246,6248],{"className":6247,"ariaHidden":1831},[1830],[1788,6249,6251,6254],{"className":6250},[1835],[1788,6252],{"className":6253,"style":1950},[1839],[1788,6255,1938],{"className":6256,"style":1954},[1844,1845]," 阶主子式是不唯一的，而 ",[1099,6259,6260,6288],{},[1788,6261,6263,6276],{"className":6262},[1791],[1788,6264,6266],{"className":6265},[1795],[1797,6267,6268],{"xmlns":1799},[1801,6269,6270,6274],{},[1804,6271,6272],{},[1807,6273,1938],{},[1823,6275,1938],{"encoding":1825},[1788,6277,6279],{"className":6278,"ariaHidden":1831},[1830],[1788,6280,6282,6285],{"className":6281},[1835],[1788,6283],{"className":6284,"style":1950},[1839],[1788,6286,1938],{"className":6287,"style":1954},[1844,1845]," 阶顺序主子式是唯一的","。用在判断",[1099,6291,6292],{},"二次型正定","上，下面会讲。",[1091,6295,6297],{"id":6296},"四-矩阵的秩","四. 矩阵的秩",[1096,6299,6300,6301],{},"① ",[1788,6302,6304,6349],{"className":6303},[1791],[1788,6305,6307],{"className":6306},[1795],[1797,6308,6309],{"xmlns":1799},[1801,6310,6311,6346],{},[1804,6312,6313,6315,6318,6320,6322,6324,6326,6328,6331,6334,6337,6339,6341,6343],{},[1985,6314,1987],{},[1811,6316,6317],{},"≤",[1807,6319,2421],{},[1811,6321,1977],{"stretchy":1976},[1807,6323,2290],{},[1811,6325,1990],{"stretchy":1976},[1811,6327,6317],{},[1807,6329,6330],{},"min",[1811,6332,6333],{},"⁡",[1811,6335,6336],{"stretchy":1976},"{",[1807,6338,4911],{},[1811,6340,2430],{"separator":1831},[1807,6342,2301],{},[1811,6344,6345],{"stretchy":1976},"}",[1823,6347,6348],{"encoding":1825},"0\\leq r(A)\\leq\\min\\{m,n\\}",[1788,6350,6352,6371,6398],{"className":6351,"ariaHidden":1831},[1830],[1788,6353,6355,6359,6362,6365,6368],{"className":6354},[1835],[1788,6356],{"className":6357,"style":6358},[1839],"height:0.7804em;vertical-align:-0.136em;",[1788,6360,1987],{"className":6361},[1844],[1788,6363],{"className":6364,"style":1851},[1850],[1788,6366,6317],{"className":6367},[1855],[1788,6369],{"className":6370,"style":1851},[1850],[1788,6372,6374,6377,6380,6383,6386,6389,6392,6395],{"className":6373},[1835],[1788,6375],{"className":6376,"style":2003},[1839],[1788,6378,2421],{"className":6379,"style":1846},[1844,1845],[1788,6381,1977],{"className":6382},[2013],[1788,6384,2290],{"className":6385},[1844,1845],[1788,6387,1990],{"className":6388},[2079],[1788,6390],{"className":6391,"style":1851},[1850],[1788,6393,6317],{"className":6394},[1855],[1788,6396],{"className":6397,"style":1851},[1850],[1788,6399,6401,6404,6408,6411,6414,6417,6420,6423],{"className":6400},[1835],[1788,6402],{"className":6403,"style":2003},[1839],[1788,6405,6330],{"className":6406},[6407],"mop",[1788,6409,6336],{"className":6410},[2013],[1788,6412,4911],{"className":6413},[1844,1845],[1788,6415,2430],{"className":6416},[2474],[1788,6418],{"className":6419,"style":2478},[1850],[1788,6421,2301],{"className":6422},[1844,1845],[1788,6424,6345],{"className":6425},[2079],[1096,6427,6428,6429],{},"② ",[1788,6430,6432,6476],{"className":6431},[1791],[1788,6433,6435],{"className":6434},[1795],[1797,6436,6437],{"xmlns":1799},[1801,6438,6439,6473],{},[1804,6440,6441,6443,6445,6447,6449,6451,6453,6455,6457,6459,6461,6463,6465,6467,6469,6471],{},[1807,6442,2421],{},[1811,6444,1977],{"stretchy":1976},[1807,6446,1938],{},[1807,6448,2290],{},[1811,6450,1990],{"stretchy":1976},[1811,6452,1813],{},[1807,6454,2421],{},[1811,6456,1977],{"stretchy":1976},[1807,6458,2290],{},[1811,6460,1990],{"stretchy":1976},[1971,6462,1973],{},[1811,6464,1977],{"stretchy":1976},[1807,6466,1938],{},[1811,6468,1983],{"mathvariant":1982},[1985,6470,1987],{},[1811,6472,1990],{"stretchy":1976},[1823,6474,6475],{"encoding":1825},"r(kA)=r(A)\\ (k\\neq 0)",[1788,6477,6479,6509,6578],{"className":6478,"ariaHidden":1831},[1830],[1788,6480,6482,6485,6488,6491,6494,6497,6500,6503,6506],{"className":6481},[1835],[1788,6483],{"className":6484,"style":2003},[1839],[1788,6486,2421],{"className":6487,"style":1846},[1844,1845],[1788,6489,1977],{"className":6490},[2013],[1788,6492,1938],{"className":6493,"style":1954},[1844,1845],[1788,6495,2290],{"className":6496},[1844,1845],[1788,6498,1990],{"className":6499},[2079],[1788,6501],{"className":6502,"style":1851},[1850],[1788,6504,1813],{"className":6505},[1855],[1788,6507],{"className":6508,"style":1851},[1850],[1788,6510,6512,6515,6518,6521,6524,6527,6530,6533,6536,6539,6575],{"className":6511},[1835],[1788,6513],{"className":6514,"style":2003},[1839],[1788,6516,2421],{"className":6517,"style":1846},[1844,1845],[1788,6519,1977],{"className":6520},[2013],[1788,6522,2290],{"className":6523},[1844,1845],[1788,6525,1990],{"className":6526},[2079],[1788,6528,1973],{"className":6529},[1850],[1788,6531,1977],{"className":6532},[2013],[1788,6534,1938],{"className":6535,"style":1954},[1844,1845],[1788,6537],{"className":6538,"style":1851},[1850],[1788,6540,6542,6569,6572],{"className":6541},[1855],[1788,6543,6545],{"className":6544},[1855],[1788,6546,6548],{"className":6547},[1844,2029],[1788,6549,6551],{"className":6550},[2033],[1788,6552,6554,6557,6566],{"className":6553},[2037],[1788,6555],{"className":6556,"style":2041},[1839],[1788,6558,6560],{"className":6559},[2045],[1788,6561,6563],{"className":6562},[1844],[1788,6564,2052],{"className":6565},[1855],[1788,6567],{"className":6568},[2056],[1788,6570],{"className":6571},[1850,2060],[1788,6573,1813],{"className":6574},[1855],[1788,6576],{"className":6577,"style":1851},[1850],[1788,6579,6581,6584,6587],{"className":6580},[1835],[1788,6582],{"className":6583,"style":2003},[1839],[1788,6585,1987],{"className":6586},[1844],[1788,6588,1990],{"className":6589},[2079],[1096,6591,6592,6593],{},"③ ",[1788,6594,6596,6646],{"className":6595},[1791],[1788,6597,6599],{"className":6598},[1795],[1797,6600,6601],{"xmlns":1799},[1801,6602,6603,6643],{},[1804,6604,6605,6607,6609,6611,6613,6615,6617,6619,6621,6623,6625,6627,6629,6631,6633,6635,6637,6639,6641],{},[1807,6606,2421],{},[1811,6608,1977],{"stretchy":1976},[1807,6610,2290],{},[1807,6612,3841],{},[1811,6614,1990],{"stretchy":1976},[1811,6616,6317],{},[1807,6618,6330],{},[1811,6620,6333],{},[1811,6622,6336],{"stretchy":1976},[1807,6624,2421],{},[1811,6626,1977],{"stretchy":1976},[1807,6628,2290],{},[1811,6630,1990],{"stretchy":1976},[1811,6632,2430],{"separator":1831},[1807,6634,2421],{},[1811,6636,1977],{"stretchy":1976},[1807,6638,3841],{},[1811,6640,1990],{"stretchy":1976},[1811,6642,6345],{"stretchy":1976},[1823,6644,6645],{"encoding":1825},"r(AB)\\leq\\min\\{r(A),r(B)\\}",[1788,6647,6649,6679],{"className":6648,"ariaHidden":1831},[1830],[1788,6650,6652,6655,6658,6661,6664,6667,6670,6673,6676],{"className":6651},[1835],[1788,6653],{"className":6654,"style":2003},[1839],[1788,6656,2421],{"className":6657,"style":1846},[1844,1845],[1788,6659,1977],{"className":6660},[2013],[1788,6662,2290],{"className":6663},[1844,1845],[1788,6665,3841],{"className":6666,"style":3866},[1844,1845],[1788,6668,1990],{"className":6669},[2079],[1788,6671],{"className":6672,"style":1851},[1850],[1788,6674,6317],{"className":6675},[1855],[1788,6677],{"className":6678,"style":1851},[1850],[1788,6680,6682,6685,6688,6691,6694,6697,6700,6703,6706,6709,6712,6715,6718],{"className":6681},[1835],[1788,6683],{"className":6684,"style":2003},[1839],[1788,6686,6330],{"className":6687},[6407],[1788,6689,6336],{"className":6690},[2013],[1788,6692,2421],{"className":6693,"style":1846},[1844,1845],[1788,6695,1977],{"className":6696},[2013],[1788,6698,2290],{"className":6699},[1844,1845],[1788,6701,1990],{"className":6702},[2079],[1788,6704,2430],{"className":6705},[2474],[1788,6707],{"className":6708,"style":2478},[1850],[1788,6710,2421],{"className":6711,"style":1846},[1844,1845],[1788,6713,1977],{"className":6714},[2013],[1788,6716,3841],{"className":6717,"style":3866},[1844,1845],[1788,6719,6721],{"className":6720},[2079],")}",[1096,6723,6724,6725],{},"④ ",[1788,6726,6728,6772],{"className":6727},[1791],[1788,6729,6731],{"className":6730},[1795],[1797,6732,6733],{"xmlns":1799},[1801,6734,6735,6769],{},[1804,6736,6737,6739,6741,6743,6745,6747,6749,6751,6753,6755,6757,6759,6761,6763,6765,6767],{},[1807,6738,2421],{},[1811,6740,1977],{"stretchy":1976},[1807,6742,2290],{},[1811,6744,2899],{},[1807,6746,3841],{},[1811,6748,1990],{"stretchy":1976},[1811,6750,6317],{},[1807,6752,2421],{},[1811,6754,1977],{"stretchy":1976},[1807,6756,2290],{},[1811,6758,1990],{"stretchy":1976},[1811,6760,2899],{},[1807,6762,2421],{},[1811,6764,1977],{"stretchy":1976},[1807,6766,3841],{},[1811,6768,1990],{"stretchy":1976},[1823,6770,6771],{"encoding":1825},"r(A+B)\\leq r(A)+r(B)",[1788,6773,6775,6799,6820,6847],{"className":6774,"ariaHidden":1831},[1830],[1788,6776,6778,6781,6784,6787,6790,6793,6796],{"className":6777},[1835],[1788,6779],{"className":6780,"style":2003},[1839],[1788,6782,2421],{"className":6783,"style":1846},[1844,1845],[1788,6785,1977],{"className":6786},[2013],[1788,6788,2290],{"className":6789},[1844,1845],[1788,6791],{"className":6792,"style":3029},[1850],[1788,6794,2899],{"className":6795},[3033],[1788,6797],{"className":6798,"style":3029},[1850],[1788,6800,6802,6805,6808,6811,6814,6817],{"className":6801},[1835],[1788,6803],{"className":6804,"style":2003},[1839],[1788,6806,3841],{"className":6807,"style":3866},[1844,1845],[1788,6809,1990],{"className":6810},[2079],[1788,6812],{"className":6813,"style":1851},[1850],[1788,6815,6317],{"className":6816},[1855],[1788,6818],{"className":6819,"style":1851},[1850],[1788,6821,6823,6826,6829,6832,6835,6838,6841,6844],{"className":6822},[1835],[1788,6824],{"className":6825,"style":2003},[1839],[1788,6827,2421],{"className":6828,"style":1846},[1844,1845],[1788,6830,1977],{"className":6831},[2013],[1788,6833,2290],{"className":6834},[1844,1845],[1788,6836,1990],{"className":6837},[2079],[1788,6839],{"className":6840,"style":3029},[1850],[1788,6842,2899],{"className":6843},[3033],[1788,6845],{"className":6846,"style":3029},[1850],[1788,6848,6850,6853,6856,6859,6862],{"className":6849},[1835],[1788,6851],{"className":6852,"style":2003},[1839],[1788,6854,2421],{"className":6855,"style":1846},[1844,1845],[1788,6857,1977],{"className":6858},[2013],[1788,6860,3841],{"className":6861,"style":3866},[1844,1845],[1788,6863,1990],{"className":6864},[2079],[1096,6866,6867,6868,2389],{},"⑤ Sylvester 秩不等式：",[1788,6869,6871,6918],{"className":6870},[1791],[1788,6872,6874],{"className":6873},[1795],[1797,6875,6876],{"xmlns":1799},[1801,6877,6878,6915],{},[1804,6879,6880,6882,6884,6886,6888,6890,6893,6895,6897,6899,6901,6903,6905,6907,6909,6911,6913],{},[1807,6881,2421],{},[1811,6883,1977],{"stretchy":1976},[1807,6885,2290],{},[1807,6887,3841],{},[1811,6889,1990],{"stretchy":1976},[1811,6891,6892],{},"≥",[1807,6894,2421],{},[1811,6896,1977],{"stretchy":1976},[1807,6898,2290],{},[1811,6900,1990],{"stretchy":1976},[1811,6902,2899],{},[1807,6904,2421],{},[1811,6906,1977],{"stretchy":1976},[1807,6908,3841],{},[1811,6910,1990],{"stretchy":1976},[1811,6912,3250],{},[1807,6914,2301],{},[1823,6916,6917],{"encoding":1825},"r(AB)\\geq r(A)+r(B)-n",[1788,6919,6921,6951,6978,7005],{"className":6920,"ariaHidden":1831},[1830],[1788,6922,6924,6927,6930,6933,6936,6939,6942,6945,6948],{"className":6923},[1835],[1788,6925],{"className":6926,"style":2003},[1839],[1788,6928,2421],{"className":6929,"style":1846},[1844,1845],[1788,6931,1977],{"className":6932},[2013],[1788,6934,2290],{"className":6935},[1844,1845],[1788,6937,3841],{"className":6938,"style":3866},[1844,1845],[1788,6940,1990],{"className":6941},[2079],[1788,6943],{"className":6944,"style":1851},[1850],[1788,6946,6892],{"className":6947},[1855],[1788,6949],{"className":6950,"style":1851},[1850],[1788,6952,6954,6957,6960,6963,6966,6969,6972,6975],{"className":6953},[1835],[1788,6955],{"className":6956,"style":2003},[1839],[1788,6958,2421],{"className":6959,"style":1846},[1844,1845],[1788,6961,1977],{"className":6962},[2013],[1788,6964,2290],{"className":6965},[1844,1845],[1788,6967,1990],{"className":6968},[2079],[1788,6970],{"className":6971,"style":3029},[1850],[1788,6973,2899],{"className":6974},[3033],[1788,6976],{"className":6977,"style":3029},[1850],[1788,6979,6981,6984,6987,6990,6993,6996,6999,7002],{"className":6980},[1835],[1788,6982],{"className":6983,"style":2003},[1839],[1788,6985,2421],{"className":6986,"style":1846},[1844,1845],[1788,6988,1977],{"className":6989},[2013],[1788,6991,3841],{"className":6992,"style":3866},[1844,1845],[1788,6994,1990],{"className":6995},[2079],[1788,6997],{"className":6998,"style":3029},[1850],[1788,7000,3250],{"className":7001},[3033],[1788,7003],{"className":7004,"style":3029},[1850],[1788,7006,7008,7011],{"className":7007},[1835],[1788,7009],{"className":7010,"style":3114},[1839],[1788,7012,2301],{"className":7013},[1844,1845],[1096,7015,7016],{},[2114,7017],{"alt":7018,"src":7019},"矩阵的秩（五）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be17ac8a1.png",[1096,7021,7022],{},[1099,7023,7024,7112,7113,7215],{},[1788,7025,7027,7055],{"className":7026},[1791],[1788,7028,7030],{"className":7029},[1795],[1797,7031,7032],{"xmlns":1799},[1801,7033,7034,7052],{},[1804,7035,7036,7038,7040,7042,7044,7046,7048,7050],{},[1807,7037,2421],{},[1811,7039,1977],{"stretchy":1976},[1807,7041,2290],{},[1811,7043,1990],{"stretchy":1976},[1811,7045,1813],{},[1807,7047,2301],{},[1811,7049,3250],{},[1985,7051,2906],{},[1823,7053,7054],{"encoding":1825},"r(A)=n-1",[1788,7056,7058,7085,7103],{"className":7057,"ariaHidden":1831},[1830],[1788,7059,7061,7064,7067,7070,7073,7076,7079,7082],{"className":7060},[1835],[1788,7062],{"className":7063,"style":2003},[1839],[1788,7065,2421],{"className":7066,"style":1846},[1844,1845],[1788,7068,1977],{"className":7069},[2013],[1788,7071,2290],{"className":7072},[1844,1845],[1788,7074,1990],{"className":7075},[2079],[1788,7077],{"className":7078,"style":1851},[1850],[1788,7080,1813],{"className":7081},[1855],[1788,7083],{"className":7084,"style":1851},[1850],[1788,7086,7088,7091,7094,7097,7100],{"className":7087},[1835],[1788,7089],{"className":7090,"style":4190},[1839],[1788,7092,2301],{"className":7093},[1844,1845],[1788,7095],{"className":7096,"style":3029},[1850],[1788,7098,3250],{"className":7099},[3033],[1788,7101],{"className":7102,"style":3029},[1850],[1788,7104,7106,7109],{"className":7105},[1835],[1788,7107],{"className":7108,"style":4209},[1839],[1788,7110,2906],{"className":7111},[1844]," 时 ",[1788,7114,7116,7146],{"className":7115},[1791],[1788,7117,7119],{"className":7118},[1795],[1797,7120,7121],{"xmlns":1799},[1801,7122,7123,7143],{},[1804,7124,7125,7127,7129,7137,7139,7141],{},[1807,7126,2421],{},[1811,7128,1977],{"stretchy":1976},[1815,7130,7131,7133],{},[1807,7132,2290],{},[1811,7134,7136],{"lspace":7135,"rspace":7135},"0em","∗",[1811,7138,1990],{"stretchy":1976},[1811,7140,1813],{},[1985,7142,2906],{},[1823,7144,7145],{"encoding":1825},"r(A^{*})=1",[1788,7147,7149,7206],{"className":7148,"ariaHidden":1831},[1830],[1788,7150,7152,7155,7158,7161,7194,7197,7200,7203],{"className":7151},[1835],[1788,7153],{"className":7154,"style":2003},[1839],[1788,7156,2421],{"className":7157,"style":1846},[1844,1845],[1788,7159,1977],{"className":7160},[2013],[1788,7162,7164,7167],{"className":7163},[1844],[1788,7165,2290],{"className":7166},[1844,1845],[1788,7168,7170],{"className":7169},[1875],[1788,7171,7173],{"className":7172},[1879],[1788,7174,7176],{"className":7175},[1883],[1788,7177,7180],{"className":7178,"style":7179},[1887],"height:0.6887em;",[1788,7181,7182,7185],{"style":1890},[1788,7183],{"className":7184,"style":1895},[1894],[1788,7186,7188],{"className":7187},[1899,1900,1901,1902],[1788,7189,7191],{"className":7190},[1844,1902],[1788,7192,7136],{"className":7193},[1844,1902],[1788,7195,1990],{"className":7196},[2079],[1788,7198],{"className":7199,"style":1851},[1850],[1788,7201,1813],{"className":7202},[1855],[1788,7204],{"className":7205,"style":1851},[1850],[1788,7207,7209,7212],{"className":7208},[1835],[1788,7210],{"className":7211,"style":4209},[1839],[1788,7213,2906],{"className":7214},[1844]," 的证明：",[1096,7217,7218],{},[2114,7219],{"alt":7220,"src":7221},"r(A*)=1的证明","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1808208.jpeg",[1096,7223,7224],{},"进而可得出一个重要结论：",[1096,7226,7227,7228,2080,7402,2389],{},"若 ",[1788,7229,7231,7273],{"className":7230},[1791],[1788,7232,7234],{"className":7233},[1795],[1797,7235,7236],{"xmlns":1799},[1801,7237,7238,7270],{},[1804,7239,7240,7252,7265,7267],{},[2881,7241,7242,7244],{},[1807,7243,2290],{},[1804,7245,7246,7248,7250],{},[1807,7247,4911],{},[1811,7249,4914],{},[1807,7251,2301],{},[2881,7253,7254,7256],{},[1807,7255,3841],{},[1804,7257,7258,7260,7262],{},[1807,7259,2301],{},[1811,7261,4914],{},[1807,7263,7264],{},"s",[1811,7266,1813],{},[1807,7268,7269],{},"O",[1823,7271,7272],{"encoding":1825},"A_{m\\times n}B_{n\\times s}=O",[1788,7274,7276,7393],{"className":7275,"ariaHidden":1831},[1830],[1788,7277,7279,7283,7334,7384,7387,7390],{"className":7278},[1835],[1788,7280],{"className":7281,"style":7282},[1839],"height:0.8917em;vertical-align:-0.2083em;",[1788,7284,7286,7289],{"className":7285},[1844],[1788,7287,2290],{"className":7288},[1844,1845],[1788,7290,7292],{"className":7291},[1875],[1788,7293,7295,7325],{"className":7294},[1879,2931],[1788,7296,7298,7322],{"className":7297},[1883],[1788,7299,7302],{"className":7300,"style":7301},[1887],"height:0.2583em;",[1788,7303,7304,7307],{"style":4072},[1788,7305],{"className":7306,"style":1895},[1894],[1788,7308,7310],{"className":7309},[1899,1900,1901,1902],[1788,7311,7313,7316,7319],{"className":7312},[1844,1902],[1788,7314,4911],{"className":7315},[1844,1845,1902],[1788,7317,4914],{"className":7318},[3033,1902],[1788,7320,2301],{"className":7321},[1844,1845,1902],[1788,7323,2958],{"className":7324},[2957],[1788,7326,7328],{"className":7327},[1883],[1788,7329,7332],{"className":7330,"style":7331},[1887],"height:0.2083em;",[1788,7333],{},[1788,7335,7337,7340],{"className":7336},[1844],[1788,7338,3841],{"className":7339,"style":3866},[1844,1845],[1788,7341,7343],{"className":7342},[1875],[1788,7344,7346,7376],{"className":7345},[1879,2931],[1788,7347,7349,7373],{"className":7348},[1883],[1788,7350,7352],{"className":7351,"style":7301},[1887],[1788,7353,7355,7358],{"style":7354},"top:-2.55em;margin-left:-0.0502em;margin-right:0.05em;",[1788,7356],{"className":7357,"style":1895},[1894],[1788,7359,7361],{"className":7360},[1899,1900,1901,1902],[1788,7362,7364,7367,7370],{"className":7363},[1844,1902],[1788,7365,2301],{"className":7366},[1844,1845,1902],[1788,7368,4914],{"className":7369},[3033,1902],[1788,7371,7264],{"className":7372},[1844,1845,1902],[1788,7374,2958],{"className":7375},[2957],[1788,7377,7379],{"className":7378},[1883],[1788,7380,7382],{"className":7381,"style":7331},[1887],[1788,7383],{},[1788,7385],{"className":7386,"style":1851},[1850],[1788,7388,1813],{"className":7389},[1855],[1788,7391],{"className":7392,"style":1851},[1850],[1788,7394,7396,7399],{"className":7395},[1835],[1788,7397],{"className":7398,"style":1840},[1839],[1788,7400,7269],{"className":7401,"style":1846},[1844,1845],[1788,7403,7405,7439],{"className":7404},[1791],[1788,7406,7408],{"className":7407},[1795],[1797,7409,7410],{"xmlns":1799},[1801,7411,7412,7436],{},[1804,7413,7414,7416,7418,7420,7422,7424,7426,7428,7430,7432,7434],{},[1807,7415,2421],{},[1811,7417,1977],{"stretchy":1976},[1807,7419,2290],{},[1811,7421,1990],{"stretchy":1976},[1811,7423,2899],{},[1807,7425,2421],{},[1811,7427,1977],{"stretchy":1976},[1807,7429,3841],{},[1811,7431,1990],{"stretchy":1976},[1811,7433,6317],{},[1807,7435,2301],{},[1823,7437,7438],{"encoding":1825},"r(A)+r(B)\\leq n",[1788,7440,7442,7469,7496],{"className":7441,"ariaHidden":1831},[1830],[1788,7443,7445,7448,7451,7454,7457,7460,7463,7466],{"className":7444},[1835],[1788,7446],{"className":7447,"style":2003},[1839],[1788,7449,2421],{"className":7450,"style":1846},[1844,1845],[1788,7452,1977],{"className":7453},[2013],[1788,7455,2290],{"className":7456},[1844,1845],[1788,7458,1990],{"className":7459},[2079],[1788,7461],{"className":7462,"style":3029},[1850],[1788,7464,2899],{"className":7465},[3033],[1788,7467],{"className":7468,"style":3029},[1850],[1788,7470,7472,7475,7478,7481,7484,7487,7490,7493],{"className":7471},[1835],[1788,7473],{"className":7474,"style":2003},[1839],[1788,7476,2421],{"className":7477,"style":1846},[1844,1845],[1788,7479,1977],{"className":7480},[2013],[1788,7482,3841],{"className":7483,"style":3866},[1844,1845],[1788,7485,1990],{"className":7486},[2079],[1788,7488],{"className":7489,"style":1851},[1850],[1788,7491,6317],{"className":7492},[1855],[1788,7494],{"className":7495,"style":1851},[1850],[1788,7497,7499,7502],{"className":7498},[1835],[1788,7500],{"className":7501,"style":3114},[1839],[1788,7503,2301],{"className":7504},[1844,1845],[1096,7506,7507,7508,7564],{},"所以，看到 ",[1788,7509,7511,7531],{"className":7510},[1791],[1788,7512,7514],{"className":7513},[1795],[1797,7515,7516],{"xmlns":1799},[1801,7517,7518,7528],{},[1804,7519,7520,7522,7524,7526],{},[1807,7521,2290],{},[1807,7523,3841],{},[1811,7525,1813],{},[1807,7527,7269],{},[1823,7529,7530],{"encoding":1825},"AB=O",[1788,7532,7534,7555],{"className":7533,"ariaHidden":1831},[1830],[1788,7535,7537,7540,7543,7546,7549,7552],{"className":7536},[1835],[1788,7538],{"className":7539,"style":1840},[1839],[1788,7541,2290],{"className":7542},[1844,1845],[1788,7544,3841],{"className":7545,"style":3866},[1844,1845],[1788,7547],{"className":7548,"style":1851},[1850],[1788,7550,1813],{"className":7551},[1855],[1788,7553],{"className":7554,"style":1851},[1850],[1788,7556,7558,7561],{"className":7557},[1835],[1788,7559],{"className":7560,"style":1840},[1839],[1788,7562,7269],{"className":7563,"style":1846},[1844,1845]," 就要想到两个结论：",[1096,7566,7567],{},[2114,7568],{"alt":7569,"src":7570},"看到AB=O","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be18c42df.png",[1096,7572,7573,7574,4896,7602,7652,7653,7698,7699,7727,7728,7756],{},"⑥ 设 ",[1788,7575,7577,7590],{"className":7576},[1791],[1788,7578,7580],{"className":7579},[1795],[1797,7581,7582],{"xmlns":1799},[1801,7583,7584,7588],{},[1804,7585,7586],{},[1807,7587,2290],{},[1823,7589,2290],{"encoding":1825},[1788,7591,7593],{"className":7592,"ariaHidden":1831},[1830],[1788,7594,7596,7599],{"className":7595},[1835],[1788,7597],{"className":7598,"style":1840},[1839],[1788,7600,2290],{"className":7601},[1844,1845],[1788,7603,7605,7622],{"className":7604},[1791],[1788,7606,7608],{"className":7607},[1795],[1797,7609,7610],{"xmlns":1799},[1801,7611,7612,7620],{},[1804,7613,7614,7616,7618],{},[1807,7615,4911],{},[1811,7617,4914],{},[1807,7619,2301],{},[1823,7621,4919],{"encoding":1825},[1788,7623,7625,7643],{"className":7624,"ariaHidden":1831},[1830],[1788,7626,7628,7631,7634,7637,7640],{"className":7627},[1835],[1788,7629],{"className":7630,"style":4190},[1839],[1788,7632,4911],{"className":7633},[1844,1845],[1788,7635],{"className":7636,"style":3029},[1850],[1788,7638,4914],{"className":7639},[3033],[1788,7641],{"className":7642,"style":3029},[1850],[1788,7644,7646,7649],{"className":7645},[1835],[1788,7647],{"className":7648,"style":3114},[1839],[1788,7650,2301],{"className":7651},[1844,1845]," 矩阵，",[1788,7654,7656,7676],{"className":7655},[1791],[1788,7657,7659],{"className":7658},[1795],[1797,7660,7661],{"xmlns":1799},[1801,7662,7663,7673],{},[1804,7664,7665,7668,7670],{},[1807,7666,7667],{},"P",[1811,7669,2430],{"separator":1831},[1807,7671,7672],{},"Q",[1823,7674,7675],{"encoding":1825},"P,Q",[1788,7677,7679],{"className":7678,"ariaHidden":1831},[1830],[1788,7680,7682,7686,7689,7692,7695],{"className":7681},[1835],[1788,7683],{"className":7684,"style":7685},[1839],"height:0.8778em;vertical-align:-0.1944em;",[1788,7687,7667],{"className":7688,"style":1909},[1844,1845],[1788,7690,2430],{"className":7691},[2474],[1788,7693],{"className":7694,"style":2478},[1850],[1788,7696,7672],{"className":7697},[1844,1845]," 分别是 ",[1788,7700,7702,7715],{"className":7701},[1791],[1788,7703,7705],{"className":7704},[1795],[1797,7706,7707],{"xmlns":1799},[1801,7708,7709,7713],{},[1804,7710,7711],{},[1807,7712,4911],{},[1823,7714,4911],{"encoding":1825},[1788,7716,7718],{"className":7717,"ariaHidden":1831},[1830],[1788,7719,7721,7724],{"className":7720},[1835],[1788,7722],{"className":7723,"style":3114},[1839],[1788,7725,4911],{"className":7726},[1844,1845]," 阶、",[1788,7729,7731,7744],{"className":7730},[1791],[1788,7732,7734],{"className":7733},[1795],[1797,7735,7736],{"xmlns":1799},[1801,7737,7738,7742],{},[1804,7739,7740],{},[1807,7741,2301],{},[1823,7743,2301],{"encoding":1825},[1788,7745,7747],{"className":7746,"ariaHidden":1831},[1830],[1788,7748,7750,7753],{"className":7749},[1835],[1788,7751],{"className":7752,"style":3114},[1839],[1788,7754,2301],{"className":7755},[1844,1845]," 阶可逆矩阵，则",[1096,7758,7759],{},[1788,7760,7762,7820],{"className":7761},[1791],[1788,7763,7765],{"className":7764},[1795],[1797,7766,7767],{"xmlns":1799},[1801,7768,7769,7817],{},[1804,7770,7771,7773,7775,7777,7779,7781,7783,7785,7787,7789,7791,7793,7795,7797,7799,7801,7803,7805,7807,7809,7811,7813,7815],{},[1807,7772,2421],{},[1811,7774,1977],{"stretchy":1976},[1807,7776,2290],{},[1811,7778,1990],{"stretchy":1976},[1811,7780,1813],{},[1807,7782,2421],{},[1811,7784,1977],{"stretchy":1976},[1807,7786,7667],{},[1807,7788,2290],{},[1811,7790,1990],{"stretchy":1976},[1811,7792,1813],{},[1807,7794,2421],{},[1811,7796,1977],{"stretchy":1976},[1807,7798,2290],{},[1807,7800,7672],{},[1811,7802,1990],{"stretchy":1976},[1811,7804,1813],{},[1807,7806,2421],{},[1811,7808,1977],{"stretchy":1976},[1807,7810,7667],{},[1807,7812,2290],{},[1807,7814,7672],{},[1811,7816,1990],{"stretchy":1976},[1823,7818,7819],{"encoding":1825},"r(A)=r(PA)=r(AQ)=r(PAQ)",[1788,7821,7823,7850,7880,7910],{"className":7822,"ariaHidden":1831},[1830],[1788,7824,7826,7829,7832,7835,7838,7841,7844,7847],{"className":7825},[1835],[1788,7827],{"className":7828,"style":2003},[1839],[1788,7830,2421],{"className":7831,"style":1846},[1844,1845],[1788,7833,1977],{"className":7834},[2013],[1788,7836,2290],{"className":7837},[1844,1845],[1788,7839,1990],{"className":7840},[2079],[1788,7842],{"className":7843,"style":1851},[1850],[1788,7845,1813],{"className":7846},[1855],[1788,7848],{"className":7849,"style":1851},[1850],[1788,7851,7853,7856,7859,7862,7865,7868,7871,7874,7877],{"className":7852},[1835],[1788,7854],{"className":7855,"style":2003},[1839],[1788,7857,2421],{"className":7858,"style":1846},[1844,1845],[1788,7860,1977],{"className":7861},[2013],[1788,7863,7667],{"className":7864,"style":1909},[1844,1845],[1788,7866,2290],{"className":7867},[1844,1845],[1788,7869,1990],{"className":7870},[2079],[1788,7872],{"className":7873,"style":1851},[1850],[1788,7875,1813],{"className":7876},[1855],[1788,7878],{"className":7879,"style":1851},[1850],[1788,7881,7883,7886,7889,7892,7895,7898,7901,7904,7907],{"className":7882},[1835],[1788,7884],{"className":7885,"style":2003},[1839],[1788,7887,2421],{"className":7888,"style":1846},[1844,1845],[1788,7890,1977],{"className":7891},[2013],[1788,7893,2290],{"className":7894},[1844,1845],[1788,7896,7672],{"className":7897},[1844,1845],[1788,7899,1990],{"className":7900},[2079],[1788,7902],{"className":7903,"style":1851},[1850],[1788,7905,1813],{"className":7906},[1855],[1788,7908],{"className":7909,"style":1851},[1850],[1788,7911,7913,7916,7919,7922,7925,7928,7931],{"className":7912},[1835],[1788,7914],{"className":7915,"style":2003},[1839],[1788,7917,2421],{"className":7918,"style":1846},[1844,1845],[1788,7920,1977],{"className":7921},[2013],[1788,7923,7667],{"className":7924,"style":1909},[1844,1845],[1788,7926,2290],{"className":7927},[1844,1845],[1788,7929,7672],{"className":7930},[1844,1845],[1788,7932,1990],{"className":7933},[2079],[1096,7935,7936,7937,2389],{},"⑦ ",[1788,7938,7940,8006],{"className":7939},[1791],[1788,7941,7943],{"className":7942},[1795],[1797,7944,7945],{"xmlns":1799},[1801,7946,7947,8003],{},[1804,7948,7949,7951,7953,7955,7957,7959,7961,7963,7969,7971,7973,7975,7977,7979,7985,7987,7989,7991,7993,7999,8001],{},[1807,7950,2421],{},[1811,7952,1977],{"stretchy":1976},[1807,7954,2290],{},[1811,7956,1990],{"stretchy":1976},[1811,7958,1813],{},[1807,7960,2421],{},[1811,7962,1977],{"stretchy":1976},[1815,7964,7965,7967],{},[1807,7966,2290],{},[1807,7968,1821],{},[1811,7970,1990],{"stretchy":1976},[1811,7972,1813],{},[1807,7974,2421],{},[1811,7976,1977],{"stretchy":1976},[1807,7978,2290],{},[1815,7980,7981,7983],{},[1807,7982,2290],{},[1807,7984,1821],{},[1811,7986,1990],{"stretchy":1976},[1811,7988,1813],{},[1807,7990,2421],{},[1811,7992,1977],{"stretchy":1976},[1815,7994,7995,7997],{},[1807,7996,2290],{},[1807,7998,1821],{},[1807,8000,2290],{},[1811,8002,1990],{"stretchy":1976},[1823,8004,8005],{"encoding":1825},"r(A)=r(A^{T})=r(AA^{T})=r(A^{T}A)",[1788,8007,8009,8036,8093,8152],{"className":8008,"ariaHidden":1831},[1830],[1788,8010,8012,8015,8018,8021,8024,8027,8030,8033],{"className":8011},[1835],[1788,8013],{"className":8014,"style":2003},[1839],[1788,8016,2421],{"className":8017,"style":1846},[1844,1845],[1788,8019,1977],{"className":8020},[2013],[1788,8022,2290],{"className":8023},[1844,1845],[1788,8025,1990],{"className":8026},[2079],[1788,8028],{"className":8029,"style":1851},[1850],[1788,8031,1813],{"className":8032},[1855],[1788,8034],{"className":8035,"style":1851},[1850],[1788,8037,8039,8043,8046,8049,8081,8084,8087,8090],{"className":8038},[1835],[1788,8040],{"className":8041,"style":8042},[1839],"height:1.0913em;vertical-align:-0.25em;",[1788,8044,2421],{"className":8045,"style":1846},[1844,1845],[1788,8047,1977],{"className":8048},[2013],[1788,8050,8052,8055],{"className":8051},[1844],[1788,8053,2290],{"className":8054},[1844,1845],[1788,8056,8058],{"className":8057},[1875],[1788,8059,8061],{"className":8060},[1879],[1788,8062,8064],{"className":8063},[1883],[1788,8065,8067],{"className":8066,"style":1865},[1887],[1788,8068,8069,8072],{"style":1890},[1788,8070],{"className":8071,"style":1895},[1894],[1788,8073,8075],{"className":8074},[1899,1900,1901,1902],[1788,8076,8078],{"className":8077},[1844,1902],[1788,8079,1821],{"className":8080,"style":1909},[1844,1845,1902],[1788,8082,1990],{"className":8083},[2079],[1788,8085],{"className":8086,"style":1851},[1850],[1788,8088,1813],{"className":8089},[1855],[1788,8091],{"className":8092,"style":1851},[1850],[1788,8094,8096,8099,8102,8105,8108,8140,8143,8146,8149],{"className":8095},[1835],[1788,8097],{"className":8098,"style":8042},[1839],[1788,8100,2421],{"className":8101,"style":1846},[1844,1845],[1788,8103,1977],{"className":8104},[2013],[1788,8106,2290],{"className":8107},[1844,1845],[1788,8109,8111,8114],{"className":8110},[1844],[1788,8112,2290],{"className":8113},[1844,1845],[1788,8115,8117],{"className":8116},[1875],[1788,8118,8120],{"className":8119},[1879],[1788,8121,8123],{"className":8122},[1883],[1788,8124,8126],{"className":8125,"style":1865},[1887],[1788,8127,8128,8131],{"style":1890},[1788,8129],{"className":8130,"style":1895},[1894],[1788,8132,8134],{"className":8133},[1899,1900,1901,1902],[1788,8135,8137],{"className":8136},[1844,1902],[1788,8138,1821],{"className":8139,"style":1909},[1844,1845,1902],[1788,8141,1990],{"className":8142},[2079],[1788,8144],{"className":8145,"style":1851},[1850],[1788,8147,1813],{"className":8148},[1855],[1788,8150],{"className":8151,"style":1851},[1850],[1788,8153,8155,8158,8161,8164,8196,8199],{"className":8154},[1835],[1788,8156],{"className":8157,"style":8042},[1839],[1788,8159,2421],{"className":8160,"style":1846},[1844,1845],[1788,8162,1977],{"className":8163},[2013],[1788,8165,8167,8170],{"className":8166},[1844],[1788,8168,2290],{"className":8169},[1844,1845],[1788,8171,8173],{"className":8172},[1875],[1788,8174,8176],{"className":8175},[1879],[1788,8177,8179],{"className":8178},[1883],[1788,8180,8182],{"className":8181,"style":1865},[1887],[1788,8183,8184,8187],{"style":1890},[1788,8185],{"className":8186,"style":1895},[1894],[1788,8188,8190],{"className":8189},[1899,1900,1901,1902],[1788,8191,8193],{"className":8192},[1844,1902],[1788,8194,1821],{"className":8195,"style":1909},[1844,1845,1902],[1788,8197,2290],{"className":8198},[1844,1845],[1788,8200,1990],{"className":8201},[2079],[1096,8203,8204],{},"关于⑤的例题：",[1096,8206,8207],{},[2114,8208],{"alt":8209,"src":8210},"秩的例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1968a2a.png",[1096,8212,8213,8214,8271,8272,8345],{},"为什么 ",[1788,8215,8217,8238],{"className":8216},[1791],[1788,8218,8220],{"className":8219},[1795],[1797,8221,8222],{"xmlns":1799},[1801,8223,8224,8235],{},[1804,8225,8226,8228,8231,8233],{},[1807,8227,2290],{},[1807,8229,8230],{},"x",[1811,8232,1813],{},[1807,8234,2444],{},[1823,8236,8237],{"encoding":1825},"Ax=b",[1788,8239,8241,8262],{"className":8240,"ariaHidden":1831},[1830],[1788,8242,8244,8247,8250,8253,8256,8259],{"className":8243},[1835],[1788,8245],{"className":8246,"style":1840},[1839],[1788,8248,2290],{"className":8249},[1844,1845],[1788,8251,8230],{"className":8252},[1844,1845],[1788,8254],{"className":8255,"style":1851},[1850],[1788,8257,1813],{"className":8258},[1855],[1788,8260],{"className":8261,"style":1851},[1850],[1788,8263,8265,8268],{"className":8264},[1835],[1788,8266],{"className":8267,"style":1950},[1839],[1788,8269,2444],{"className":8270},[1844,1845]," 有 ",[1788,8273,8275,8297],{"className":8274},[1791],[1788,8276,8278],{"className":8277},[1795],[1797,8279,8280],{"xmlns":1799},[1801,8281,8282,8294],{},[1804,8283,8284,8286,8288,8290,8292],{},[1807,8285,2301],{},[1811,8287,3250],{},[1807,8289,2421],{},[1811,8291,2899],{},[1985,8293,2906],{},[1823,8295,8296],{"encoding":1825},"n-r+1",[1788,8298,8300,8318,8336],{"className":8299,"ariaHidden":1831},[1830],[1788,8301,8303,8306,8309,8312,8315],{"className":8302},[1835],[1788,8304],{"className":8305,"style":4190},[1839],[1788,8307,2301],{"className":8308},[1844,1845],[1788,8310],{"className":8311,"style":3029},[1850],[1788,8313,3250],{"className":8314},[3033],[1788,8316],{"className":8317,"style":3029},[1850],[1788,8319,8321,8324,8327,8330,8333],{"className":8320},[1835],[1788,8322],{"className":8323,"style":4190},[1839],[1788,8325,2421],{"className":8326,"style":1846},[1844,1845],[1788,8328],{"className":8329,"style":3029},[1850],[1788,8331,2899],{"className":8332},[3033],[1788,8334],{"className":8335,"style":3029},[1850],[1788,8337,8339,8342],{"className":8338},[1835],[1788,8340],{"className":8341,"style":4209},[1839],[1788,8343,2906],{"className":8344},[1844]," 个线性无关的解：",[1096,8347,8348],{},[2114,8349],{"alt":8350,"src":8351},"为什么有n-r+1个线性无关解","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1a401a8.png",[1091,8353,8355],{"id":8354},"五-常用特征值与特征向量","五. 常用特征值与特征向量",[1096,8357,8358],{},[2114,8359],{"alt":8360,"src":8361},"常用特征值与特征向量","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1977f3e.png",[1096,8363,8364],{},[1099,8365,8366],{},"注意这样一道例题：",[1096,8368,8369],{},[2114,8370],{"alt":8371,"src":8372},"特征值例题（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1989394.png",[1096,8374,8375],{},[2114,8376],{"alt":8377,"src":8378},"特征值例题（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1a81805.png",[1096,8380,8381],{},[2114,8382],{"alt":8383,"src":8384},"特征值例题（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1a5656c.png",[1096,8386,8387],{},[2114,8388],{"alt":8389,"src":8390},"特征值例题（四）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1a9ec52.png",[1096,8392,8393],{},"关于特征值的一些提示：",[1096,8395,8396],{},[2114,8397],{"alt":8398,"src":8399},"特征值提示","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1bd81d8.png",[1091,8401,8403],{"id":8402},"六-矩阵向量组方程组","六. 矩阵，向量组，方程组",[1096,8405,8406],{},[1099,8407,8408],{},"矩阵与向量组",[1912,8410,8411,8608,8722],{},[1096,8412,6300,8413,8416,8417,8445,8446,8497,8498,8526,8527,8497,8579,8607],{},[1099,8414,8415],{},"向量组","是由有限个相同维数的行向量或者列向量组成，其中向量是由 ",[1788,8418,8420,8433],{"className":8419},[1791],[1788,8421,8423],{"className":8422},[1795],[1797,8424,8425],{"xmlns":1799},[1801,8426,8427,8431],{},[1804,8428,8429],{},[1807,8430,2301],{},[1823,8432,2301],{"encoding":1825},[1788,8434,8436],{"className":8435,"ariaHidden":1831},[1830],[1788,8437,8439,8442],{"className":8438},[1835],[1788,8440],{"className":8441,"style":3114},[1839],[1788,8443,2301],{"className":8444},[1844,1845]," 个实数组成的有序数组，是一个 ",[1788,8447,8449,8467],{"className":8448},[1791],[1788,8450,8452],{"className":8451},[1795],[1797,8453,8454],{"xmlns":1799},[1801,8455,8456,8464],{},[1804,8457,8458,8460,8462],{},[1807,8459,2301],{},[1811,8461,4914],{},[1985,8463,2906],{},[1823,8465,8466],{"encoding":1825},"n\\times 1",[1788,8468,8470,8488],{"className":8469,"ariaHidden":1831},[1830],[1788,8471,8473,8476,8479,8482,8485],{"className":8472},[1835],[1788,8474],{"className":8475,"style":4190},[1839],[1788,8477,2301],{"className":8478},[1844,1845],[1788,8480],{"className":8481,"style":3029},[1850],[1788,8483,4914],{"className":8484},[3033],[1788,8486],{"className":8487,"style":3029},[1850],[1788,8489,8491,8494],{"className":8490},[1835],[1788,8492],{"className":8493,"style":4209},[1839],[1788,8495,2906],{"className":8496},[1844]," 的矩阵（",[1788,8499,8501,8514],{"className":8500},[1791],[1788,8502,8504],{"className":8503},[1795],[1797,8505,8506],{"xmlns":1799},[1801,8507,8508,8512],{},[1804,8509,8510],{},[1807,8511,2301],{},[1823,8513,2301],{"encoding":1825},[1788,8515,8517],{"className":8516,"ariaHidden":1831},[1830],[1788,8518,8520,8523],{"className":8519},[1835],[1788,8521],{"className":8522,"style":3114},[1839],[1788,8524,2301],{"className":8525},[1844,1845]," 维列向量）或是一个 ",[1788,8528,8530,8548],{"className":8529},[1791],[1788,8531,8533],{"className":8532},[1795],[1797,8534,8535],{"xmlns":1799},[1801,8536,8537,8545],{},[1804,8538,8539,8541,8543],{},[1985,8540,2906],{},[1811,8542,4914],{},[1807,8544,2301],{},[1823,8546,8547],{"encoding":1825},"1\\times n",[1788,8549,8551,8570],{"className":8550,"ariaHidden":1831},[1830],[1788,8552,8554,8558,8561,8564,8567],{"className":8553},[1835],[1788,8555],{"className":8556,"style":8557},[1839],"height:0.7278em;vertical-align:-0.0833em;",[1788,8559,2906],{"className":8560},[1844],[1788,8562],{"className":8563,"style":3029},[1850],[1788,8565,4914],{"className":8566},[3033],[1788,8568],{"className":8569,"style":3029},[1850],[1788,8571,8573,8576],{"className":8572},[1835],[1788,8574],{"className":8575,"style":3114},[1839],[1788,8577,2301],{"className":8578},[1844,1845],[1788,8580,8582,8595],{"className":8581},[1791],[1788,8583,8585],{"className":8584},[1795],[1797,8586,8587],{"xmlns":1799},[1801,8588,8589,8593],{},[1804,8590,8591],{},[1807,8592,2301],{},[1823,8594,2301],{"encoding":1825},[1788,8596,8598],{"className":8597,"ariaHidden":1831},[1830],[1788,8599,8601,8604],{"className":8600},[1835],[1788,8602],{"className":8603,"style":3114},[1839],[1788,8605,2301],{"className":8606},[1844,1845]," 维行向量）。",[1096,8609,6428,8610,8613,8614,8664,8665,5280,8693,8721],{},[1099,8611,8612],{},"矩阵","是由 ",[1788,8615,8617,8634],{"className":8616},[1791],[1788,8618,8620],{"className":8619},[1795],[1797,8621,8622],{"xmlns":1799},[1801,8623,8624,8632],{},[1804,8625,8626,8628,8630],{},[1807,8627,4911],{},[1811,8629,4914],{},[1807,8631,2301],{},[1823,8633,4919],{"encoding":1825},[1788,8635,8637,8655],{"className":8636,"ariaHidden":1831},[1830],[1788,8638,8640,8643,8646,8649,8652],{"className":8639},[1835],[1788,8641],{"className":8642,"style":4190},[1839],[1788,8644,4911],{"className":8645},[1844,1845],[1788,8647],{"className":8648,"style":3029},[1850],[1788,8650,4914],{"className":8651},[3033],[1788,8653],{"className":8654,"style":3029},[1850],[1788,8656,8658,8661],{"className":8657},[1835],[1788,8659],{"className":8660,"style":3114},[1839],[1788,8662,2301],{"className":8663},[1844,1845]," 个数排列成 ",[1788,8666,8668,8681],{"className":8667},[1791],[1788,8669,8671],{"className":8670},[1795],[1797,8672,8673],{"xmlns":1799},[1801,8674,8675,8679],{},[1804,8676,8677],{},[1807,8678,4911],{},[1823,8680,4911],{"encoding":1825},[1788,8682,8684],{"className":8683,"ariaHidden":1831},[1830],[1788,8685,8687,8690],{"className":8686},[1835],[1788,8688],{"className":8689,"style":3114},[1839],[1788,8691,4911],{"className":8692},[1844,1845],[1788,8694,8696,8709],{"className":8695},[1791],[1788,8697,8699],{"className":8698},[1795],[1797,8700,8701],{"xmlns":1799},[1801,8702,8703,8707],{},[1804,8704,8705],{},[1807,8706,2301],{},[1823,8708,2301],{"encoding":1825},[1788,8710,8712],{"className":8711,"ariaHidden":1831},[1830],[1788,8713,8715,8718],{"className":8714},[1835],[1788,8716],{"className":8717,"style":3114},[1839],[1788,8719,2301],{"className":8720},[1844,1845]," 列的数表。",[1096,8723,8724,8727,8728,8756,8757,8785,8786,8814],{},[1099,8725,8726],{},"一个向量组可以看作是一个矩阵的列（或行）向量集合","。如果一个矩阵有 ",[1788,8729,8731,8744],{"className":8730},[1791],[1788,8732,8734],{"className":8733},[1795],[1797,8735,8736],{"xmlns":1799},[1801,8737,8738,8742],{},[1804,8739,8740],{},[1807,8741,2301],{},[1823,8743,2301],{"encoding":1825},[1788,8745,8747],{"className":8746,"ariaHidden":1831},[1830],[1788,8748,8750,8753],{"className":8749},[1835],[1788,8751],{"className":8752,"style":3114},[1839],[1788,8754,2301],{"className":8755},[1844,1845]," 列，那么这 ",[1788,8758,8760,8773],{"className":8759},[1791],[1788,8761,8763],{"className":8762},[1795],[1797,8764,8765],{"xmlns":1799},[1801,8766,8767,8771],{},[1804,8768,8769],{},[1807,8770,2301],{},[1823,8772,2301],{"encoding":1825},[1788,8774,8776],{"className":8775,"ariaHidden":1831},[1830],[1788,8777,8779,8782],{"className":8778},[1835],[1788,8780],{"className":8781,"style":3114},[1839],[1788,8783,2301],{"className":8784},[1844,1845]," 列就可以看作是一个由 ",[1788,8787,8789,8802],{"className":8788},[1791],[1788,8790,8792],{"className":8791},[1795],[1797,8793,8794],{"xmlns":1799},[1801,8795,8796,8800],{},[1804,8797,8798],{},[1807,8799,2301],{},[1823,8801,2301],{"encoding":1825},[1788,8803,8805],{"className":8804,"ariaHidden":1831},[1830],[1788,8806,8808,8811],{"className":8807},[1835],[1788,8809],{"className":8810,"style":3114},[1839],[1788,8812,2301],{"className":8813},[1844,1845]," 个向量组成的向量组。反过来，一个矩阵也可以看作是由其列（或行）向量组成的向量组。",[1780,8816,8818],{"id":8817},"_1-怎么判断两个矩阵等价","1. 怎么判断两个矩阵等价",[1912,8820,8821,8929,8936],{},[1096,8822,8823,8824,8852,8853,8881,8882,8885,8886,8928],{},"矩阵等价的前提：",[1788,8825,8827,8840],{"className":8826},[1791],[1788,8828,8830],{"className":8829},[1795],[1797,8831,8832],{"xmlns":1799},[1801,8833,8834,8838],{},[1804,8835,8836],{},[1807,8837,2290],{},[1823,8839,2290],{"encoding":1825},[1788,8841,8843],{"className":8842,"ariaHidden":1831},[1830],[1788,8844,8846,8849],{"className":8845},[1835],[1788,8847],{"className":8848,"style":1840},[1839],[1788,8850,2290],{"className":8851},[1844,1845]," 与 ",[1788,8854,8856,8869],{"className":8855},[1791],[1788,8857,8859],{"className":8858},[1795],[1797,8860,8861],{"xmlns":1799},[1801,8862,8863,8867],{},[1804,8864,8865],{},[1807,8866,3841],{},[1823,8868,3841],{"encoding":1825},[1788,8870,8872],{"className":8871,"ariaHidden":1831},[1830],[1788,8873,8875,8878],{"className":8874},[1835],[1788,8876],{"className":8877,"style":1840},[1839],[1788,8879,3841],{"className":8880,"style":3866},[1844,1845]," 是",[1099,8883,8884],{},"同型","矩阵，即 ",[1788,8887,8889,8907],{"className":8888},[1791],[1788,8890,8892],{"className":8891},[1795],[1797,8893,8894],{"xmlns":1799},[1801,8895,8896,8904],{},[1804,8897,8898,8900,8902],{},[1807,8899,2290],{},[1811,8901,2430],{"separator":1831},[1807,8903,3841],{},[1823,8905,8906],{"encoding":1825},"A,B",[1788,8908,8910],{"className":8909,"ariaHidden":1831},[1830],[1788,8911,8913,8916,8919,8922,8925],{"className":8912},[1835],[1788,8914],{"className":8915,"style":7685},[1839],[1788,8917,2290],{"className":8918},[1844,1845],[1788,8920,2430],{"className":8921},[2474],[1788,8923],{"className":8924,"style":2478},[1850],[1788,8926,3841],{"className":8927,"style":3866},[1844,1845]," 行数、列数相同。",[1096,8930,8931,8932,8935],{},"矩阵等价的",[1099,8933,8934],{},"充要条件","：",[1096,8937,6300,8938,9019,9020,9061,9062],{},[1788,8939,8941,8971],{"className":8940},[1791],[1788,8942,8944],{"className":8943},[1795],[1797,8945,8946],{"xmlns":1799},[1801,8947,8948,8968],{},[1804,8949,8950,8952,8954,8956,8958,8960,8962,8964,8966],{},[1807,8951,2421],{},[1811,8953,1977],{"stretchy":1976},[1807,8955,2290],{},[1811,8957,1990],{"stretchy":1976},[1811,8959,1813],{},[1807,8961,2421],{},[1811,8963,1977],{"stretchy":1976},[1807,8965,3841],{},[1811,8967,1990],{"stretchy":1976},[1823,8969,8970],{"encoding":1825},"r(A)=r(B)",[1788,8972,8974,9001],{"className":8973,"ariaHidden":1831},[1830],[1788,8975,8977,8980,8983,8986,8989,8992,8995,8998],{"className":8976},[1835],[1788,8978],{"className":8979,"style":2003},[1839],[1788,8981,2421],{"className":8982,"style":1846},[1844,1845],[1788,8984,1977],{"className":8985},[2013],[1788,8987,2290],{"className":8988},[1844,1845],[1788,8990,1990],{"className":8991},[2079],[1788,8993],{"className":8994,"style":1851},[1850],[1788,8996,1813],{"className":8997},[1855],[1788,8999],{"className":9000,"style":1851},[1850],[1788,9002,9004,9007,9010,9013,9016],{"className":9003},[1835],[1788,9005],{"className":9006,"style":2003},[1839],[1788,9008,2421],{"className":9009,"style":1846},[1844,1845],[1788,9011,1977],{"className":9012},[2013],[1788,9014,3841],{"className":9015,"style":3866},[1844,1845],[1788,9017,1990],{"className":9018},[2079],"\n② 存在可逆矩阵 ",[1788,9021,9023,9040],{"className":9022},[1791],[1788,9024,9026],{"className":9025},[1795],[1797,9027,9028],{"xmlns":1799},[1801,9029,9030,9038],{},[1804,9031,9032,9034,9036],{},[1807,9033,7667],{},[1811,9035,2430],{"separator":1831},[1807,9037,7672],{},[1823,9039,7675],{"encoding":1825},[1788,9041,9043],{"className":9042,"ariaHidden":1831},[1830],[1788,9044,9046,9049,9052,9055,9058],{"className":9045},[1835],[1788,9047],{"className":9048,"style":7685},[1839],[1788,9050,7667],{"className":9051,"style":1909},[1844,1845],[1788,9053,2430],{"className":9054},[2474],[1788,9056],{"className":9057,"style":2478},[1850],[1788,9059,7672],{"className":9060},[1844,1845],"，使得 ",[1788,9063,9065,9087],{"className":9064},[1791],[1788,9066,9068],{"className":9067},[1795],[1797,9069,9070],{"xmlns":1799},[1801,9071,9072,9084],{},[1804,9073,9074,9076,9078,9080,9082],{},[1807,9075,7667],{},[1807,9077,2290],{},[1807,9079,7672],{},[1811,9081,1813],{},[1807,9083,3841],{},[1823,9085,9086],{"encoding":1825},"PAQ=B",[1788,9088,9090,9114],{"className":9089,"ariaHidden":1831},[1830],[1788,9091,9093,9096,9099,9102,9105,9108,9111],{"className":9092},[1835],[1788,9094],{"className":9095,"style":7685},[1839],[1788,9097,7667],{"className":9098,"style":1909},[1844,1845],[1788,9100,2290],{"className":9101},[1844,1845],[1788,9103,7672],{"className":9104},[1844,1845],[1788,9106],{"className":9107,"style":1851},[1850],[1788,9109,1813],{"className":9110},[1855],[1788,9112],{"className":9113,"style":1851},[1850],[1788,9115,9117,9120],{"className":9116},[1835],[1788,9118],{"className":9119,"style":1840},[1839],[1788,9121,3841],{"className":9122,"style":3866},[1844,1845],[1780,9124,9126],{"id":9125},"_2-怎么判断两个向量组是等价向量组","2. 怎么判断两个向量组是等价向量组",[1912,9128,9129,9177,9800],{},[1096,9130,9131,9132,9173,9174,2389],{},"向量组等价的前提：",[1788,9133,9135,9152],{"className":9134},[1791],[1788,9136,9138],{"className":9137},[1795],[1797,9139,9140],{"xmlns":1799},[1801,9141,9142,9150],{},[1804,9143,9144,9146,9148],{},[1807,9145,2290],{},[1811,9147,2430],{"separator":1831},[1807,9149,3841],{},[1823,9151,8906],{"encoding":1825},[1788,9153,9155],{"className":9154,"ariaHidden":1831},[1830],[1788,9156,9158,9161,9164,9167,9170],{"className":9157},[1835],[1788,9159],{"className":9160,"style":7685},[1839],[1788,9162,2290],{"className":9163},[1844,1845],[1788,9165,2430],{"className":9166},[2474],[1788,9168],{"className":9169,"style":2478},[1850],[1788,9171,3841],{"className":9172,"style":3866},[1844,1845]," 矩阵",[1099,9175,9176],{},"同维",[1096,9178,7227,9179,3086,9487,9797,9798,8935],{},[1788,9180,9182,9249],{"className":9181},[1791],[1788,9183,9185],{"className":9184},[1795],[1797,9186,9187],{"xmlns":1799},[1801,9188,9189,9246],{},[1804,9190,9191,9193,9195,9198,9200,9202,9204,9206,9212,9214,9220,9222,9228,9230,9237,9239,9242,9244],{},[1807,9192,2421],{},[1811,9194,1977],{"stretchy":1976},[1807,9196,9197],{"mathvariant":1982},"I",[1811,9199,1990],{"stretchy":1976},[1811,9201,1813],{},[1807,9203,2421],{},[1811,9205,1977],{"stretchy":1976},[2881,9207,9208,9210],{},[1807,9209,3101],{},[1985,9211,2906],{},[1811,9213,2430],{"separator":1831},[2881,9215,9216,9218],{},[1807,9217,3101],{},[1985,9219,2896],{},[1811,9221,2430],{"separator":1831},[2881,9223,9224,9226],{},[1807,9225,3101],{},[1985,9227,2887],{},[1811,9229,2430],{"separator":1831},[2881,9231,9232,9234],{},[1807,9233,3101],{},[1985,9235,9236],{},"4",[1811,9238,2430],{"separator":1831},[1811,9240,9241],{},"⋯",[1971,9243,2433],{},[1811,9245,1990],{"stretchy":1976},[1823,9247,9248],{"encoding":1825},"r(\\mathrm{I})=r(\\alpha_1,\\alpha_2,\\alpha_3,\\alpha_4,\\cdots)",[1788,9250,9252,9280],{"className":9251,"ariaHidden":1831},[1830],[1788,9253,9255,9258,9261,9264,9268,9271,9274,9277],{"className":9254},[1835],[1788,9256],{"className":9257,"style":2003},[1839],[1788,9259,2421],{"className":9260,"style":1846},[1844,1845],[1788,9262,1977],{"className":9263},[2013],[1788,9265,9197],{"className":9266},[1844,9267],"mathrm",[1788,9269,1990],{"className":9270},[2079],[1788,9272],{"className":9273,"style":1851},[1850],[1788,9275,1813],{"className":9276},[1855],[1788,9278],{"className":9279,"style":1851},[1850],[1788,9281,9283,9286,9289,9292,9333,9336,9339,9379,9382,9385,9425,9428,9431,9471,9474,9477,9481,9484],{"className":9282},[1835],[1788,9284],{"className":9285,"style":2003},[1839],[1788,9287,2421],{"className":9288,"style":1846},[1844,1845],[1788,9290,1977],{"className":9291},[2013],[1788,9293,9295,9298],{"className":9294},[1844],[1788,9296,3101],{"className":9297,"style":3118},[1844,1845],[1788,9299,9301],{"className":9300},[1875],[1788,9302,9304,9325],{"className":9303},[1879,2931],[1788,9305,9307,9322],{"className":9306},[1883],[1788,9308,9310],{"className":9309,"style":2938},[1887],[1788,9311,9313,9316],{"style":9312},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1788,9314],{"className":9315,"style":1895},[1894],[1788,9317,9319],{"className":9318},[1899,1900,1901,1902],[1788,9320,2906],{"className":9321},[1844,1902],[1788,9323,2958],{"className":9324},[2957],[1788,9326,9328],{"className":9327},[1883],[1788,9329,9331],{"className":9330,"style":2965},[1887],[1788,9332],{},[1788,9334,2430],{"className":9335},[2474],[1788,9337],{"className":9338,"style":2478},[1850],[1788,9340,9342,9345],{"className":9341},[1844],[1788,9343,3101],{"className":9344,"style":3118},[1844,1845],[1788,9346,9348],{"className":9347},[1875],[1788,9349,9351,9371],{"className":9350},[1879,2931],[1788,9352,9354,9368],{"className":9353},[1883],[1788,9355,9357],{"className":9356,"style":2938},[1887],[1788,9358,9359,9362],{"style":9312},[1788,9360],{"className":9361,"style":1895},[1894],[1788,9363,9365],{"className":9364},[1899,1900,1901,1902],[1788,9366,2896],{"className":9367},[1844,1902],[1788,9369,2958],{"className":9370},[2957],[1788,9372,9374],{"className":9373},[1883],[1788,9375,9377],{"className":9376,"style":2965},[1887],[1788,9378],{},[1788,9380,2430],{"className":9381},[2474],[1788,9383],{"className":9384,"style":2478},[1850],[1788,9386,9388,9391],{"className":9387},[1844],[1788,9389,3101],{"className":9390,"style":3118},[1844,1845],[1788,9392,9394],{"className":9393},[1875],[1788,9395,9397,9417],{"className":9396},[1879,2931],[1788,9398,9400,9414],{"className":9399},[1883],[1788,9401,9403],{"className":9402,"style":2938},[1887],[1788,9404,9405,9408],{"style":9312},[1788,9406],{"className":9407,"style":1895},[1894],[1788,9409,9411],{"className":9410},[1899,1900,1901,1902],[1788,9412,2887],{"className":9413},[1844,1902],[1788,9415,2958],{"className":9416},[2957],[1788,9418,9420],{"className":9419},[1883],[1788,9421,9423],{"className":9422,"style":2965},[1887],[1788,9424],{},[1788,9426,2430],{"className":9427},[2474],[1788,9429],{"className":9430,"style":2478},[1850],[1788,9432,9434,9437],{"className":9433},[1844],[1788,9435,3101],{"className":9436,"style":3118},[1844,1845],[1788,9438,9440],{"className":9439},[1875],[1788,9441,9443,9463],{"className":9442},[1879,2931],[1788,9444,9446,9460],{"className":9445},[1883],[1788,9447,9449],{"className":9448,"style":2938},[1887],[1788,9450,9451,9454],{"style":9312},[1788,9452],{"className":9453,"style":1895},[1894],[1788,9455,9457],{"className":9456},[1899,1900,1901,1902],[1788,9458,9236],{"className":9459},[1844,1902],[1788,9461,2958],{"className":9462},[2957],[1788,9464,9466],{"className":9465},[1883],[1788,9467,9469],{"className":9468,"style":2965},[1887],[1788,9470],{},[1788,9472,2430],{"className":9473},[2474],[1788,9475],{"className":9476,"style":2478},[1850],[1788,9478,9241],{"className":9479},[9480],"minner",[1788,9482],{"className":9483,"style":2478},[1850],[1788,9485,1990],{"className":9486},[2079],[1788,9488,9490,9558],{"className":9489},[1791],[1788,9491,9493],{"className":9492},[1795],[1797,9494,9495],{"xmlns":1799},[1801,9496,9497,9555],{},[1804,9498,9499,9501,9503,9509,9511,9513,9515,9517,9523,9525,9531,9533,9539,9541,9547,9549,9551,9553],{},[1807,9500,2421],{},[1811,9502,1977],{"stretchy":1976},[1804,9504,9505,9507],{},[1807,9506,9197],{"mathvariant":1982},[1807,9508,9197],{"mathvariant":1982},[1811,9510,1990],{"stretchy":1976},[1811,9512,1813],{},[1807,9514,2421],{},[1811,9516,1977],{"stretchy":1976},[2881,9518,9519,9521],{},[1807,9520,2850],{},[1985,9522,2906],{},[1811,9524,2430],{"separator":1831},[2881,9526,9527,9529],{},[1807,9528,2850],{},[1985,9530,2896],{},[1811,9532,2430],{"separator":1831},[2881,9534,9535,9537],{},[1807,9536,2850],{},[1985,9538,2887],{},[1811,9540,2430],{"separator":1831},[2881,9542,9543,9545],{},[1807,9544,2850],{},[1985,9546,9236],{},[1811,9548,2430],{"separator":1831},[1811,9550,9241],{},[1971,9552,2433],{},[1811,9554,1990],{"stretchy":1976},[1823,9556,9557],{"encoding":1825},"r(\\mathrm{II})=r(\\beta_1,\\beta_2,\\beta_3,\\beta_4,\\cdots)",[1788,9559,9561,9592],{"className":9560,"ariaHidden":1831},[1830],[1788,9562,9564,9567,9570,9573,9580,9583,9586,9589],{"className":9563},[1835],[1788,9565],{"className":9566,"style":2003},[1839],[1788,9568,2421],{"className":9569,"style":1846},[1844,1845],[1788,9571,1977],{"className":9572},[2013],[1788,9574,9576],{"className":9575},[1844],[1788,9577,9579],{"className":9578},[1844,9267],"II",[1788,9581,1990],{"className":9582},[2079],[1788,9584],{"className":9585,"style":1851},[1850],[1788,9587,1813],{"className":9588},[1855],[1788,9590],{"className":9591,"style":1851},[1850],[1788,9593,9595,9598,9601,9604,9644,9647,9650,9690,9693,9696,9736,9739,9742,9782,9785,9788,9791,9794],{"className":9594},[1835],[1788,9596],{"className":9597,"style":2003},[1839],[1788,9599,2421],{"className":9600,"style":1846},[1844,1845],[1788,9602,1977],{"className":9603},[2013],[1788,9605,9607,9610],{"className":9606},[1844],[1788,9608,2850],{"className":9609,"style":2866},[1844,1845],[1788,9611,9613],{"className":9612},[1875],[1788,9614,9616,9636],{"className":9615},[1879,2931],[1788,9617,9619,9633],{"className":9618},[1883],[1788,9620,9622],{"className":9621,"style":2938},[1887],[1788,9623,9624,9627],{"style":2941},[1788,9625],{"className":9626,"style":1895},[1894],[1788,9628,9630],{"className":9629},[1899,1900,1901,1902],[1788,9631,2906],{"className":9632},[1844,1902],[1788,9634,2958],{"className":9635},[2957],[1788,9637,9639],{"className":9638},[1883],[1788,9640,9642],{"className":9641,"style":2965},[1887],[1788,9643],{},[1788,9645,2430],{"className":9646},[2474],[1788,9648],{"className":9649,"style":2478},[1850],[1788,9651,9653,9656],{"className":9652},[1844],[1788,9654,2850],{"className":9655,"style":2866},[1844,1845],[1788,9657,9659],{"className":9658},[1875],[1788,9660,9662,9682],{"className":9661},[1879,2931],[1788,9663,9665,9679],{"className":9664},[1883],[1788,9666,9668],{"className":9667,"style":2938},[1887],[1788,9669,9670,9673],{"style":2941},[1788,9671],{"className":9672,"style":1895},[1894],[1788,9674,9676],{"className":9675},[1899,1900,1901,1902],[1788,9677,2896],{"className":9678},[1844,1902],[1788,9680,2958],{"className":9681},[2957],[1788,9683,9685],{"className":9684},[1883],[1788,9686,9688],{"className":9687,"style":2965},[1887],[1788,9689],{},[1788,9691,2430],{"className":9692},[2474],[1788,9694],{"className":9695,"style":2478},[1850],[1788,9697,9699,9702],{"className":9698},[1844],[1788,9700,2850],{"className":9701,"style":2866},[1844,1845],[1788,9703,9705],{"className":9704},[1875],[1788,9706,9708,9728],{"className":9707},[1879,2931],[1788,9709,9711,9725],{"className":9710},[1883],[1788,9712,9714],{"className":9713,"style":2938},[1887],[1788,9715,9716,9719],{"style":2941},[1788,9717],{"className":9718,"style":1895},[1894],[1788,9720,9722],{"className":9721},[1899,1900,1901,1902],[1788,9723,2887],{"className":9724},[1844,1902],[1788,9726,2958],{"className":9727},[2957],[1788,9729,9731],{"className":9730},[1883],[1788,9732,9734],{"className":9733,"style":2965},[1887],[1788,9735],{},[1788,9737,2430],{"className":9738},[2474],[1788,9740],{"className":9741,"style":2478},[1850],[1788,9743,9745,9748],{"className":9744},[1844],[1788,9746,2850],{"className":9747,"style":2866},[1844,1845],[1788,9749,9751],{"className":9750},[1875],[1788,9752,9754,9774],{"className":9753},[1879,2931],[1788,9755,9757,9771],{"className":9756},[1883],[1788,9758,9760],{"className":9759,"style":2938},[1887],[1788,9761,9762,9765],{"style":2941},[1788,9763],{"className":9764,"style":1895},[1894],[1788,9766,9768],{"className":9767},[1899,1900,1901,1902],[1788,9769,9236],{"className":9770},[1844,1902],[1788,9772,2958],{"className":9773},[2957],[1788,9775,9777],{"className":9776},[1883],[1788,9778,9780],{"className":9779,"style":2965},[1887],[1788,9781],{},[1788,9783,2430],{"className":9784},[2474],[1788,9786],{"className":9787,"style":2478},[1850],[1788,9789,9241],{"className":9790},[9480],[1788,9792],{"className":9793,"style":2478},[1850],[1788,9795,1990],{"className":9796},[2079],"，则向量组等价的",[1099,9799,8934],{},[1096,9801,6300,9802,9890,9891,9930,9931,9977,9978,9890,10066,9930,10111,10149,10150,10952,10953,11098,11099,3630,11128,11162],{},[1788,9803,9805,9839],{"className":9804},[1791],[1788,9806,9808],{"className":9807},[1795],[1797,9809,9810],{"xmlns":1799},[1801,9811,9812,9836],{},[1804,9813,9814,9816,9818,9820,9822,9824,9826,9828,9834],{},[1807,9815,2421],{},[1811,9817,1977],{"stretchy":1976},[1807,9819,9197],{"mathvariant":1982},[1811,9821,1990],{"stretchy":1976},[1811,9823,1813],{},[1807,9825,2421],{},[1811,9827,1977],{"stretchy":1976},[1804,9829,9830,9832],{},[1807,9831,9197],{"mathvariant":1982},[1807,9833,9197],{"mathvariant":1982},[1811,9835,1990],{"stretchy":1976},[1823,9837,9838],{"encoding":1825},"r(\\mathrm{I})=r(\\mathrm{II})",[1788,9840,9842,9869],{"className":9841,"ariaHidden":1831},[1830],[1788,9843,9845,9848,9851,9854,9857,9860,9863,9866],{"className":9844},[1835],[1788,9846],{"className":9847,"style":2003},[1839],[1788,9849,2421],{"className":9850,"style":1846},[1844,1845],[1788,9852,1977],{"className":9853},[2013],[1788,9855,9197],{"className":9856},[1844,9267],[1788,9858,1990],{"className":9859},[2079],[1788,9861],{"className":9862,"style":1851},[1850],[1788,9864,1813],{"className":9865},[1855],[1788,9867],{"className":9868,"style":1851},[1850],[1788,9870,9872,9875,9878,9881,9887],{"className":9871},[1835],[1788,9873],{"className":9874,"style":2003},[1839],[1788,9876,2421],{"className":9877,"style":1846},[1844,1845],[1788,9879,1977],{"className":9880},[2013],[1788,9882,9884],{"className":9883},[1844],[1788,9885,9579],{"className":9886},[1844,9267],[1788,9888,1990],{"className":9889},[2079],"，且 ",[1788,9892,9894,9912],{"className":9893},[1791],[1788,9895,9897],{"className":9896},[1795],[1797,9898,9899],{"xmlns":1799},[1801,9900,9901,9909],{},[1804,9902,9903,9905,9907],{},[1811,9904,1977],{"stretchy":1976},[1807,9906,9197],{"mathvariant":1982},[1811,9908,1990],{"stretchy":1976},[1823,9910,9911],{"encoding":1825},"(\\mathrm{I})",[1788,9913,9915],{"className":9914,"ariaHidden":1831},[1830],[1788,9916,9918,9921,9924,9927],{"className":9917},[1835],[1788,9919],{"className":9920,"style":2003},[1839],[1788,9922,1977],{"className":9923},[2013],[1788,9925,9197],{"className":9926},[1844,9267],[1788,9928,1990],{"className":9929},[2079]," 可由 ",[1788,9932,9934,9956],{"className":9933},[1791],[1788,9935,9937],{"className":9936},[1795],[1797,9938,9939],{"xmlns":1799},[1801,9940,9941,9953],{},[1804,9942,9943,9945,9951],{},[1811,9944,1977],{"stretchy":1976},[1804,9946,9947,9949],{},[1807,9948,9197],{"mathvariant":1982},[1807,9950,9197],{"mathvariant":1982},[1811,9952,1990],{"stretchy":1976},[1823,9954,9955],{"encoding":1825},"(\\mathrm{II})",[1788,9957,9959],{"className":9958,"ariaHidden":1831},[1830],[1788,9960,9962,9965,9968,9974],{"className":9961},[1835],[1788,9963],{"className":9964,"style":2003},[1839],[1788,9966,1977],{"className":9967},[2013],[1788,9969,9971],{"className":9970},[1844],[1788,9972,9579],{"className":9973},[1844,9267],[1788,9975,1990],{"className":9976},[2079]," 线性表出（单向表出即可）\n② ",[1788,9979,9981,10015],{"className":9980},[1791],[1788,9982,9984],{"className":9983},[1795],[1797,9985,9986],{"xmlns":1799},[1801,9987,9988,10012],{},[1804,9989,9990,9992,9994,10000,10002,10004,10006,10008,10010],{},[1807,9991,2421],{},[1811,9993,1977],{"stretchy":1976},[1804,9995,9996,9998],{},[1807,9997,9197],{"mathvariant":1982},[1807,9999,9197],{"mathvariant":1982},[1811,10001,1990],{"stretchy":1976},[1811,10003,1813],{},[1807,10005,2421],{},[1811,10007,1977],{"stretchy":1976},[1807,10009,9197],{"mathvariant":1982},[1811,10011,1990],{"stretchy":1976},[1823,10013,10014],{"encoding":1825},"r(\\mathrm{II})=r(\\mathrm{I})",[1788,10016,10018,10048],{"className":10017,"ariaHidden":1831},[1830],[1788,10019,10021,10024,10027,10030,10036,10039,10042,10045],{"className":10020},[1835],[1788,10022],{"className":10023,"style":2003},[1839],[1788,10025,2421],{"className":10026,"style":1846},[1844,1845],[1788,10028,1977],{"className":10029},[2013],[1788,10031,10033],{"className":10032},[1844],[1788,10034,9579],{"className":10035},[1844,9267],[1788,10037,1990],{"className":10038},[2079],[1788,10040],{"className":10041,"style":1851},[1850],[1788,10043,1813],{"className":10044},[1855],[1788,10046],{"className":10047,"style":1851},[1850],[1788,10049,10051,10054,10057,10060,10063],{"className":10050},[1835],[1788,10052],{"className":10053,"style":2003},[1839],[1788,10055,2421],{"className":10056,"style":1846},[1844,1845],[1788,10058,1977],{"className":10059},[2013],[1788,10061,9197],{"className":10062},[1844,9267],[1788,10064,1990],{"className":10065},[2079],[1788,10067,10069,10090],{"className":10068},[1791],[1788,10070,10072],{"className":10071},[1795],[1797,10073,10074],{"xmlns":1799},[1801,10075,10076,10088],{},[1804,10077,10078,10080,10086],{},[1811,10079,1977],{"stretchy":1976},[1804,10081,10082,10084],{},[1807,10083,9197],{"mathvariant":1982},[1807,10085,9197],{"mathvariant":1982},[1811,10087,1990],{"stretchy":1976},[1823,10089,9955],{"encoding":1825},[1788,10091,10093],{"className":10092,"ariaHidden":1831},[1830],[1788,10094,10096,10099,10102,10108],{"className":10095},[1835],[1788,10097],{"className":10098,"style":2003},[1839],[1788,10100,1977],{"className":10101},[2013],[1788,10103,10105],{"className":10104},[1844],[1788,10106,9579],{"className":10107},[1844,9267],[1788,10109,1990],{"className":10110},[2079],[1788,10112,10114,10131],{"className":10113},[1791],[1788,10115,10117],{"className":10116},[1795],[1797,10118,10119],{"xmlns":1799},[1801,10120,10121,10129],{},[1804,10122,10123,10125,10127],{},[1811,10124,1977],{"stretchy":1976},[1807,10126,9197],{"mathvariant":1982},[1811,10128,1990],{"stretchy":1976},[1823,10130,9911],{"encoding":1825},[1788,10132,10134],{"className":10133,"ariaHidden":1831},[1830],[1788,10135,10137,10140,10143,10146],{"className":10136},[1835],[1788,10138],{"className":10139,"style":2003},[1839],[1788,10141,1977],{"className":10142},[2013],[1788,10144,9197],{"className":10145},[1844,9267],[1788,10147,1990],{"className":10148},[2079]," 线性表出（单向表出即可）\n③ 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",[1788,10954,10956,11008],{"className":10955},[1791],[1788,10957,10959],{"className":10958},[1795],[1797,10960,10961],{"xmlns":1799},[1801,10962,10963,11005],{},[1804,10964,10965,10967,10969,10971,10973,10975,10977,10979,10985,10987,10989,10991,10993,10995,10997,11003],{},[1807,10966,2421],{},[1811,10968,1977],{"stretchy":1976},[1807,10970,9197],{"mathvariant":1982},[1811,10972,1990],{"stretchy":1976},[1811,10974,1813],{},[1807,10976,2421],{},[1811,10978,1977],{"stretchy":1976},[1804,10980,10981,10983],{},[1807,10982,9197],{"mathvariant":1982},[1807,10984,9197],{"mathvariant":1982},[1811,10986,1990],{"stretchy":1976},[1811,10988,1813],{},[1807,10990,2421],{},[1811,10992,1977],{"stretchy":1976},[1807,10994,9197],{"mathvariant":1982},[1811,10996,2430],{"separator":1831},[1804,10998,10999,11001],{},[1807,11000,9197],{"mathvariant":1982},[1807,11002,9197],{"mathvariant":1982},[1811,11004,1990],{"stretchy":1976},[1823,11006,11007],{"encoding":1825},"r(\\mathrm{I})=r(\\mathrm{II})=r(\\mathrm{I},\\mathrm{II})",[1788,11009,11011,11038,11068],{"className":11010,"ariaHidden":1831},[1830],[1788,11012,11014,11017,11020,11023,11026,11029,11032,11035],{"className":11013},[1835],[1788,11015],{"className":11016,"style":2003},[1839],[1788,11018,2421],{"className":11019,"style":1846},[1844,1845],[1788,11021,1977],{"className":11022},[2013],[1788,11024,9197],{"className":11025},[1844,9267],[1788,11027,1990],{"className":11028},[2079],[1788,11030],{"className":11031,"style":1851},[1850],[1788,11033,1813],{"className":11034},[1855],[1788,11036],{"className":11037,"style":1851},[1850],[1788,11039,11041,11044,11047,11050,11056,11059,11062,11065],{"className":11040},[1835],[1788,11042],{"className":11043,"style":2003},[1839],[1788,11045,2421],{"className":11046,"style":1846},[1844,1845],[1788,11048,1977],{"className":11049},[2013],[1788,11051,11053],{"className":11052},[1844],[1788,11054,9579],{"className":11055},[1844,9267],[1788,11057,1990],{"className":11058},[2079],[1788,11060],{"className":11061,"style":1851},[1850],[1788,11063,1813],{"className":11064},[1855],[1788,11066],{"className":11067,"style":1851},[1850],[1788,11069,11071,11074,11077,11080,11083,11086,11089,11095],{"className":11070},[1835],[1788,11072],{"className":11073,"style":2003},[1839],[1788,11075,2421],{"className":11076,"style":1846},[1844,1845],[1788,11078,1977],{"className":11079},[2013],[1788,11081,9197],{"className":11082},[1844,9267],[1788,11084,2430],{"className":11085},[2474],[1788,11087],{"className":11088,"style":2478},[1850],[1788,11090,11092],{"className":11091},[1844],[1788,11093,9579],{"className":11094},[1844,9267],[1788,11096,1990],{"className":11097},[2079],"\n④ ",[1788,11100,11102,11116],{"className":11101},[1791],[1788,11103,11105],{"className":11104},[1795],[1797,11106,11107],{"xmlns":1799},[1801,11108,11109,11113],{},[1804,11110,11111],{},[1807,11112,9197],{"mathvariant":1982},[1823,11114,11115],{"encoding":1825},"\\mathrm{I}",[1788,11117,11119],{"className":11118,"ariaHidden":1831},[1830],[1788,11120,11122,11125],{"className":11121},[1835],[1788,11123],{"className":11124,"style":1840},[1839],[1788,11126,9197],{"className":11127},[1844,9267],[1788,11129,11131,11147],{"className":11130},[1791],[1788,11132,11134],{"className":11133},[1795],[1797,11135,11136],{"xmlns":1799},[1801,11137,11138,11144],{},[1804,11139,11140,11142],{},[1807,11141,9197],{"mathvariant":1982},[1807,11143,9197],{"mathvariant":1982},[1823,11145,11146],{"encoding":1825},"\\mathrm{II}",[1788,11148,11150],{"className":11149,"ariaHidden":1831},[1830],[1788,11151,11153,11156],{"className":11152},[1835],[1788,11154],{"className":11155,"style":1840},[1839],[1788,11157,11159],{"className":11158},[1844],[1788,11160,9579],{"className":11161},[1844,9267]," 能够相互线性表示。",[1912,11164,11165,11170],{},[1096,11166,11167],{},[1099,11168,11169],{},"总结：",[1096,11171,11172,11173,8852,11201,11229,11230,11258,11259,11287],{},"① 两个矩阵 ",[1788,11174,11176,11189],{"className":11175},[1791],[1788,11177,11179],{"className":11178},[1795],[1797,11180,11181],{"xmlns":1799},[1801,11182,11183,11187],{},[1804,11184,11185],{},[1807,11186,2290],{},[1823,11188,2290],{"encoding":1825},[1788,11190,11192],{"className":11191,"ariaHidden":1831},[1830],[1788,11193,11195,11198],{"className":11194},[1835],[1788,11196],{"className":11197,"style":1840},[1839],[1788,11199,2290],{"className":11200},[1844,1845],[1788,11202,11204,11217],{"className":11203},[1791],[1788,11205,11207],{"className":11206},[1795],[1797,11208,11209],{"xmlns":1799},[1801,11210,11211,11215],{},[1804,11212,11213],{},[1807,11214,3841],{},[1823,11216,3841],{"encoding":1825},[1788,11218,11220],{"className":11219,"ariaHidden":1831},[1830],[1788,11221,11223,11226],{"className":11222},[1835],[1788,11224],{"className":11225,"style":1840},[1839],[1788,11227,3841],{"className":11228,"style":3866},[1844,1845]," 等价指的是 ",[1788,11231,11233,11246],{"className":11232},[1791],[1788,11234,11236],{"className":11235},[1795],[1797,11237,11238],{"xmlns":1799},[1801,11239,11240,11244],{},[1804,11241,11242],{},[1807,11243,2290],{},[1823,11245,2290],{"encoding":1825},[1788,11247,11249],{"className":11248,"ariaHidden":1831},[1830],[1788,11250,11252,11255],{"className":11251},[1835],[1788,11253],{"className":11254,"style":1840},[1839],[1788,11256,2290],{"className":11257},[1844,1845]," 可以通过有限次初等变换变成 ",[1788,11260,11262,11275],{"className":11261},[1791],[1788,11263,11265],{"className":11264},[1795],[1797,11266,11267],{"xmlns":1799},[1801,11268,11269,11273],{},[1804,11270,11271],{},[1807,11272,3841],{},[1823,11274,3841],{"encoding":1825},[1788,11276,11278],{"className":11277,"ariaHidden":1831},[1830],[1788,11279,11281,11284],{"className":11280},[1835],[1788,11282],{"className":11283,"style":1840},[1839],[1788,11285,3841],{"className":11286,"style":3866},[1844,1845],"。两个不同型矩阵是不可能等价的。\n② 两个向量组等价指的是它们能够互相线性表示，它们各自所含向量的个数可能是不一样的。",[1096,11289,11290],{},[1099,11291,11292],{},"例题：",[1096,11294,11295],{},[2114,11296],{"alt":11297,"src":11298},"等价向量组例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1c02c42.png",[1912,11300,11301,11499,11761,11766],{},[1096,11302,11303,11306,11307,3630,11335,11368,11369,11397,11398,8852,11426,11456,11457,11498],{},[1099,11304,11305],{},"D."," 即使 ",[1788,11308,11310,11323],{"className":11309},[1791],[1788,11311,11313],{"className":11312},[1795],[1797,11314,11315],{"xmlns":1799},[1801,11316,11317,11321],{},[1804,11318,11319],{},[1807,11320,9197],{"mathvariant":1982},[1823,11322,11115],{"encoding":1825},[1788,11324,11326],{"className":11325,"ariaHidden":1831},[1830],[1788,11327,11329,11332],{"className":11328},[1835],[1788,11330],{"className":11331,"style":1840},[1839],[1788,11333,9197],{"className":11334},[1844,9267],[1788,11336,11338,11353],{"className":11337},[1791],[1788,11339,11341],{"className":11340},[1795],[1797,11342,11343],{"xmlns":1799},[1801,11344,11345,11351],{},[1804,11346,11347,11349],{},[1807,11348,9197],{"mathvariant":1982},[1807,11350,9197],{"mathvariant":1982},[1823,11352,11146],{"encoding":1825},[1788,11354,11356],{"className":11355,"ariaHidden":1831},[1830],[1788,11357,11359,11362],{"className":11358},[1835],[1788,11360],{"className":11361,"style":1840},[1839],[1788,11363,11365],{"className":11364},[1844],[1788,11366,9579],{"className":11367},[1844,9267]," 同为 ",[1788,11370,11372,11385],{"className":11371},[1791],[1788,11373,11375],{"className":11374},[1795],[1797,11376,11377],{"xmlns":1799},[1801,11378,11379,11383],{},[1804,11380,11381],{},[1807,11382,2301],{},[1823,11384,2301],{"encoding":1825},[1788,11386,11388],{"className":11387,"ariaHidden":1831},[1830],[1788,11389,11391,11394],{"className":11390},[1835],[1788,11392],{"className":11393,"style":3114},[1839],[1788,11395,2301],{"className":11396},[1844,1845]," 维向量组，但 ",[1788,11399,11401,11414],{"className":11400},[1791],[1788,11402,11404],{"className":11403},[1795],[1797,11405,11406],{"xmlns":1799},[1801,11407,11408,11412],{},[1804,11409,11410],{},[1807,11411,7264],{},[1823,11413,7264],{"encoding":1825},[1788,11415,11417],{"className":11416,"ariaHidden":1831},[1830],[1788,11418,11420,11423],{"className":11419},[1835],[1788,11421],{"className":11422,"style":3114},[1839],[1788,11424,7264],{"className":11425},[1844,1845],[1788,11427,11429,11443],{"className":11428},[1791],[1788,11430,11432],{"className":11431},[1795],[1797,11433,11434],{"xmlns":1799},[1801,11435,11436,11441],{},[1804,11437,11438],{},[1807,11439,11440],{},"t",[1823,11442,11440],{"encoding":1825},[1788,11444,11446],{"className":11445,"ariaHidden":1831},[1830],[1788,11447,11449,11453],{"className":11448},[1835],[1788,11450],{"className":11451,"style":11452},[1839],"height:0.6151em;",[1788,11454,11440],{"className":11455},[1844,1845]," 的关系未知，也就是行数相等、列数未知，所以 ",[1788,11458,11460,11477],{"className":11459},[1791],[1788,11461,11463],{"className":11462},[1795],[1797,11464,11465],{"xmlns":1799},[1801,11466,11467,11475],{},[1804,11468,11469,11471,11473],{},[1807,11470,2290],{},[1811,11472,2430],{"separator":1831},[1807,11474,3841],{},[1823,11476,8906],{"encoding":1825},[1788,11478,11480],{"className":11479,"ariaHidden":1831},[1830],[1788,11481,11483,11486,11489,11492,11495],{"className":11482},[1835],[1788,11484],{"className":11485,"style":7685},[1839],[1788,11487,2290],{"className":11488},[1844,1845],[1788,11490,2430],{"className":11491},[2474],[1788,11493],{"className":11494,"style":2478},[1850],[1788,11496,3841],{"className":11497,"style":3866},[1844,1845]," 两个矩阵可能不同型，不能等价。",[1096,11500,11501,11504,11505,9930,11543,11588,11589,9930,11634,11672,11673,11760],{},[1099,11502,11503],{},"B."," ",[1788,11506,11508,11525],{"className":11507},[1791],[1788,11509,11511],{"className":11510},[1795],[1797,11512,11513],{"xmlns":1799},[1801,11514,11515,11523],{},[1804,11516,11517,11519,11521],{},[1811,11518,1977],{"stretchy":1976},[1807,11520,9197],{"mathvariant":1982},[1811,11522,1990],{"stretchy":1976},[1823,11524,9911],{"encoding":1825},[1788,11526,11528],{"className":11527,"ariaHidden":1831},[1830],[1788,11529,11531,11534,11537,11540],{"className":11530},[1835],[1788,11532],{"className":11533,"style":2003},[1839],[1788,11535,1977],{"className":11536},[2013],[1788,11538,9197],{"className":11539},[1844,9267],[1788,11541,1990],{"className":11542},[2079],[1788,11544,11546,11567],{"className":11545},[1791],[1788,11547,11549],{"className":11548},[1795],[1797,11550,11551],{"xmlns":1799},[1801,11552,11553,11565],{},[1804,11554,11555,11557,11563],{},[1811,11556,1977],{"stretchy":1976},[1804,11558,11559,11561],{},[1807,11560,9197],{"mathvariant":1982},[1807,11562,9197],{"mathvariant":1982},[1811,11564,1990],{"stretchy":1976},[1823,11566,9955],{"encoding":1825},[1788,11568,11570],{"className":11569,"ariaHidden":1831},[1830],[1788,11571,11573,11576,11579,11585],{"className":11572},[1835],[1788,11574],{"className":11575,"style":2003},[1839],[1788,11577,1977],{"className":11578},[2013],[1788,11580,11582],{"className":11581},[1844],[1788,11583,9579],{"className":11584},[1844,9267],[1788,11586,1990],{"className":11587},[2079]," 表示，缺少其他条件；如果加上 ",[1788,11590,11592,11613],{"className":11591},[1791],[1788,11593,11595],{"className":11594},[1795],[1797,11596,11597],{"xmlns":1799},[1801,11598,11599,11611],{},[1804,11600,11601,11603,11609],{},[1811,11602,1977],{"stretchy":1976},[1804,11604,11605,11607],{},[1807,11606,9197],{"mathvariant":1982},[1807,11608,9197],{"mathvariant":1982},[1811,11610,1990],{"stretchy":1976},[1823,11612,9955],{"encoding":1825},[1788,11614,11616],{"className":11615,"ariaHidden":1831},[1830],[1788,11617,11619,11622,11625,11631],{"className":11618},[1835],[1788,11620],{"className":11621,"style":2003},[1839],[1788,11623,1977],{"className":11624},[2013],[1788,11626,11628],{"className":11627},[1844],[1788,11629,9579],{"className":11630},[1844,9267],[1788,11632,1990],{"className":11633},[2079],[1788,11635,11637,11654],{"className":11636},[1791],[1788,11638,11640],{"className":11639},[1795],[1797,11641,11642],{"xmlns":1799},[1801,11643,11644,11652],{},[1804,11645,11646,11648,11650],{},[1811,11647,1977],{"stretchy":1976},[1807,11649,9197],{"mathvariant":1982},[1811,11651,1990],{"stretchy":1976},[1823,11653,9911],{"encoding":1825},[1788,11655,11657],{"className":11656,"ariaHidden":1831},[1830],[1788,11658,11660,11663,11666,11669],{"className":11659},[1835],[1788,11661],{"className":11662,"style":2003},[1839],[1788,11664,1977],{"className":11665},[2013],[1788,11667,9197],{"className":11668},[1844,9267],[1788,11670,1990],{"className":11671},[2079]," 线性表出，或者 ",[1788,11674,11676,11709],{"className":11675},[1791],[1788,11677,11679],{"className":11678},[1795],[1797,11680,11681],{"xmlns":1799},[1801,11682,11683,11707],{},[1804,11684,11685,11687,11689,11691,11693,11695,11697,11699,11705],{},[1807,11686,2421],{},[1811,11688,1977],{"stretchy":1976},[1807,11690,9197],{"mathvariant":1982},[1811,11692,1990],{"stretchy":1976},[1811,11694,1813],{},[1807,11696,2421],{},[1811,11698,1977],{"stretchy":1976},[1804,11700,11701,11703],{},[1807,11702,9197],{"mathvariant":1982},[1807,11704,9197],{"mathvariant":1982},[1811,11706,1990],{"stretchy":1976},[1823,11708,9838],{"encoding":1825},[1788,11710,11712,11739],{"className":11711,"ariaHidden":1831},[1830],[1788,11713,11715,11718,11721,11724,11727,11730,11733,11736],{"className":11714},[1835],[1788,11716],{"className":11717,"style":2003},[1839],[1788,11719,2421],{"className":11720,"style":1846},[1844,1845],[1788,11722,1977],{"className":11723},[2013],[1788,11725,9197],{"className":11726},[1844,9267],[1788,11728,1990],{"className":11729},[2079],[1788,11731],{"className":11732,"style":1851},[1850],[1788,11734,1813],{"className":11735},[1855],[1788,11737],{"className":11738,"style":1851},[1850],[1788,11740,11742,11745,11748,11751,11757],{"className":11741},[1835],[1788,11743],{"className":11744,"style":2003},[1839],[1788,11746,2421],{"className":11747,"style":1846},[1844,1845],[1788,11749,1977],{"className":11750},[2013],[1788,11752,11754],{"className":11753},[1844],[1788,11755,9579],{"className":11756},[1844,9267],[1788,11758,1990],{"className":11759},[2079]," 就对了。",[1096,11762,11763],{},[1099,11764,11765],{},"C 正确。",[1096,11767,11768,11504,11770,11850,11851,9930,11896,11934,11935,9930,11973,11934,12018,12162],{},[1099,11769,11305],{},[1788,11771,11773,11802],{"className":11772},[1791],[1788,11774,11776],{"className":11775},[1795],[1797,11777,11778],{"xmlns":1799},[1801,11779,11780,11800],{},[1804,11781,11782,11784,11786,11788,11790,11792,11794,11796,11798],{},[1807,11783,2421],{},[1811,11785,1977],{"stretchy":1976},[1807,11787,2290],{},[1811,11789,1990],{"stretchy":1976},[1811,11791,1813],{},[1807,11793,2421],{},[1811,11795,1977],{"stretchy":1976},[1807,11797,3841],{},[1811,11799,1990],{"stretchy":1976},[1823,11801,8970],{"encoding":1825},[1788,11803,11805,11832],{"className":11804,"ariaHidden":1831},[1830],[1788,11806,11808,11811,11814,11817,11820,11823,11826,11829],{"className":11807},[1835],[1788,11809],{"className":11810,"style":2003},[1839],[1788,11812,2421],{"className":11813,"style":1846},[1844,1845],[1788,11815,1977],{"className":11816},[2013],[1788,11818,2290],{"className":11819},[1844,1845],[1788,11821,1990],{"className":11822},[2079],[1788,11824],{"className":11825,"style":1851},[1850],[1788,11827,1813],{"className":11828},[1855],[1788,11830],{"className":11831,"style":1851},[1850],[1788,11833,11835,11838,11841,11844,11847],{"className":11834},[1835],[1788,11836],{"className":11837,"style":2003},[1839],[1788,11839,2421],{"className":11840,"style":1846},[1844,1845],[1788,11842,1977],{"className":11843},[2013],[1788,11845,3841],{"className":11846,"style":3866},[1844,1845],[1788,11848,1990],{"className":11849},[2079],"，只能推出两个向量组秩相同，缺少其他条件；如果加上 ",[1788,11852,11854,11875],{"className":11853},[1791],[1788,11855,11857],{"className":11856},[1795],[1797,11858,11859],{"xmlns":1799},[1801,11860,11861,11873],{},[1804,11862,11863,11865,11871],{},[1811,11864,1977],{"stretchy":1976},[1804,11866,11867,11869],{},[1807,11868,9197],{"mathvariant":1982},[1807,11870,9197],{"mathvariant":1982},[1811,11872,1990],{"stretchy":1976},[1823,11874,9955],{"encoding":1825},[1788,11876,11878],{"className":11877,"ariaHidden":1831},[1830],[1788,11879,11881,11884,11887,11893],{"className":11880},[1835],[1788,11882],{"className":11883,"style":2003},[1839],[1788,11885,1977],{"className":11886},[2013],[1788,11888,11890],{"className":11889},[1844],[1788,11891,9579],{"className":11892},[1844,9267],[1788,11894,1990],{"className":11895},[2079],[1788,11897,11899,11916],{"className":11898},[1791],[1788,11900,11902],{"className":11901},[1795],[1797,11903,11904],{"xmlns":1799},[1801,11905,11906,11914],{},[1804,11907,11908,11910,11912],{},[1811,11909,1977],{"stretchy":1976},[1807,11911,9197],{"mathvariant":1982},[1811,11913,1990],{"stretchy":1976},[1823,11915,9911],{"encoding":1825},[1788,11917,11919],{"className":11918,"ariaHidden":1831},[1830],[1788,11920,11922,11925,11928,11931],{"className":11921},[1835],[1788,11923],{"className":11924,"style":2003},[1839],[1788,11926,1977],{"className":11927},[2013],[1788,11929,9197],{"className":11930},[1844,9267],[1788,11932,1990],{"className":11933},[2079]," 线性表出，或 ",[1788,11936,11938,11955],{"className":11937},[1791],[1788,11939,11941],{"className":11940},[1795],[1797,11942,11943],{"xmlns":1799},[1801,11944,11945,11953],{},[1804,11946,11947,11949,11951],{},[1811,11948,1977],{"stretchy":1976},[1807,11950,9197],{"mathvariant":1982},[1811,11952,1990],{"stretchy":1976},[1823,11954,9911],{"encoding":1825},[1788,11956,11958],{"className":11957,"ariaHidden":1831},[1830],[1788,11959,11961,11964,11967,11970],{"className":11960},[1835],[1788,11962],{"className":11963,"style":2003},[1839],[1788,11965,1977],{"className":11966},[2013],[1788,11968,9197],{"className":11969},[1844,9267],[1788,11971,1990],{"className":11972},[2079],[1788,11974,11976,11997],{"className":11975},[1791],[1788,11977,11979],{"className":11978},[1795],[1797,11980,11981],{"xmlns":1799},[1801,11982,11983,11995],{},[1804,11984,11985,11987,11993],{},[1811,11986,1977],{"stretchy":1976},[1804,11988,11989,11991],{},[1807,11990,9197],{"mathvariant":1982},[1807,11992,9197],{"mathvariant":1982},[1811,11994,1990],{"stretchy":1976},[1823,11996,9955],{"encoding":1825},[1788,11998,12000],{"className":11999,"ariaHidden":1831},[1830],[1788,12001,12003,12006,12009,12015],{"className":12002},[1835],[1788,12004],{"className":12005,"style":2003},[1839],[1788,12007,1977],{"className":12008},[2013],[1788,12010,12012],{"className":12011},[1844],[1788,12013,9579],{"className":12014},[1844,9267],[1788,12016,1990],{"className":12017},[2079],[1788,12019,12021,12072],{"className":12020},[1791],[1788,12022,12024],{"className":12023},[1795],[1797,12025,12026],{"xmlns":1799},[1801,12027,12028,12070],{},[1804,12029,12030,12032,12034,12036,12038,12040,12042,12044,12050,12052,12054,12056,12058,12060,12062,12068],{},[1807,12031,2421],{},[1811,12033,1977],{"stretchy":1976},[1807,12035,9197],{"mathvariant":1982},[1811,12037,1990],{"stretchy":1976},[1811,12039,1813],{},[1807,12041,2421],{},[1811,12043,1977],{"stretchy":1976},[1804,12045,12046,12048],{},[1807,12047,9197],{"mathvariant":1982},[1807,12049,9197],{"mathvariant":1982},[1811,12051,1990],{"stretchy":1976},[1811,12053,1813],{},[1807,12055,2421],{},[1811,12057,1977],{"stretchy":1976},[1807,12059,9197],{"mathvariant":1982},[1811,12061,2430],{"separator":1831},[1804,12063,12064,12066],{},[1807,12065,9197],{"mathvariant":1982},[1807,12067,9197],{"mathvariant":1982},[1811,12069,1990],{"stretchy":1976},[1823,12071,11007],{"encoding":1825},[1788,12073,12075,12102,12132],{"className":12074,"ariaHidden":1831},[1830],[1788,12076,12078,12081,12084,12087,12090,12093,12096,12099],{"className":12077},[1835],[1788,12079],{"className":12080,"style":2003},[1839],[1788,12082,2421],{"className":12083,"style":1846},[1844,1845],[1788,12085,1977],{"className":12086},[2013],[1788,12088,9197],{"className":12089},[1844,9267],[1788,12091,1990],{"className":12092},[2079],[1788,12094],{"className":12095,"style":1851},[1850],[1788,12097,1813],{"className":12098},[1855],[1788,12100],{"className":12101,"style":1851},[1850],[1788,12103,12105,12108,12111,12114,12120,12123,12126,12129],{"className":12104},[1835],[1788,12106],{"className":12107,"style":2003},[1839],[1788,12109,2421],{"className":12110,"style":1846},[1844,1845],[1788,12112,1977],{"className":12113},[2013],[1788,12115,12117],{"className":12116},[1844],[1788,12118,9579],{"className":12119},[1844,9267],[1788,12121,1990],{"className":12122},[2079],[1788,12124],{"className":12125,"style":1851},[1850],[1788,12127,1813],{"className":12128},[1855],[1788,12130],{"className":12131,"style":1851},[1850],[1788,12133,12135,12138,12141,12144,12147,12150,12153,12159],{"className":12134},[1835],[1788,12136],{"className":12137,"style":2003},[1839],[1788,12139,2421],{"className":12140,"style":1846},[1844,1845],[1788,12142,1977],{"className":12143},[2013],[1788,12145,9197],{"className":12146},[1844,9267],[1788,12148,2430],{"className":12149},[2474],[1788,12151],{"className":12152,"style":2478},[1850],[1788,12154,12156],{"className":12155},[1844],[1788,12157,9579],{"className":12158},[1844,9267],[1788,12160,1990],{"className":12161},[2079],"，就对了。",[1780,12164,12166],{"id":12165},"_3-矩阵和向量等价的比较","3. 矩阵和向量等价的比较",[1096,12168,12169],{},[2114,12170],{"alt":12171,"src":12172},"矩阵与向量组等价的比较","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1bf17fc.png",[1096,12174,12175],{},[1099,12176,11292],{},[1096,12178,12179],{},[2114,12180],{"alt":12181,"src":12182},"矩阵与向量组等价例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1c75912.png",[1912,12184,12185,12839,12918,13420,13424,13430,13996],{},[1096,12186,12187,11504,12190,12391,12392,12580,12581,12781,12782,12838],{},[1099,12188,12189],{},"A.",[1788,12191,12193,12235],{"className":12192},[1791],[1788,12194,12196],{"className":12195},[1795],[1797,12197,12198],{"xmlns":1799},[1801,12199,12200,12232],{},[1804,12201,12202,12204,12210,12212,12218,12220,12226,12228,12230],{},[1811,12203,1977],{"stretchy":1976},[2881,12205,12206,12208],{},[1807,12207,3101],{},[1985,12209,2906],{},[1811,12211,2430],{"separator":1831},[2881,12213,12214,12216],{},[1807,12215,3101],{},[1985,12217,2896],{},[1811,12219,2430],{"separator":1831},[2881,12221,12222,12224],{},[1807,12223,3101],{},[1985,12225,2887],{},[1811,12227,2430],{"separator":1831},[1985,12229,1987],{},[1811,12231,1990],{"stretchy":1976},[1823,12233,12234],{"encoding":1825},"(\\alpha_1,\\alpha_2,\\alpha_3,0)",[1788,12236,12238],{"className":12237,"ariaHidden":1831},[1830],[1788,12239,12241,12244,12247,12287,12290,12293,12333,12336,12339,12379,12382,12385,12388],{"className":12240},[1835],[1788,12242],{"className":12243,"style":2003},[1839],[1788,12245,1977],{"className":12246},[2013],[1788,12248,12250,12253],{"className":12249},[1844],[1788,12251,3101],{"className":12252,"style":3118},[1844,1845],[1788,12254,12256],{"className":12255},[1875],[1788,12257,12259,12279],{"className":12258},[1879,2931],[1788,12260,12262,12276],{"className":12261},[1883],[1788,12263,12265],{"className":12264,"style":2938},[1887],[1788,12266,12267,12270],{"style":9312},[1788,12268],{"className":12269,"style":1895},[1894],[1788,12271,12273],{"className":12272},[1899,1900,1901,1902],[1788,12274,2906],{"className":12275},[1844,1902],[1788,12277,2958],{"className":12278},[2957],[1788,12280,12282],{"className":12281},[1883],[1788,12283,12285],{"className":12284,"style":2965},[1887],[1788,12286],{},[1788,12288,2430],{"className":12289},[2474],[1788,12291],{"className":12292,"style":2478},[1850],[1788,12294,12296,12299],{"className":12295},[1844],[1788,12297,3101],{"className":12298,"style":3118},[1844,1845],[1788,12300,12302],{"className":12301},[1875],[1788,12303,12305,12325],{"className":12304},[1879,2931],[1788,12306,12308,12322],{"className":12307},[1883],[1788,12309,12311],{"className":12310,"style":2938},[1887],[1788,12312,12313,12316],{"style":9312},[1788,12314],{"className":12315,"style":1895},[1894],[1788,12317,12319],{"className":12318},[1899,1900,1901,1902],[1788,12320,2896],{"className":12321},[1844,1902],[1788,12323,2958],{"className":12324},[2957],[1788,12326,12328],{"className":12327},[1883],[1788,12329,12331],{"className":12330,"style":2965},[1887],[1788,12332],{},[1788,12334,2430],{"className":12335},[2474],[1788,12337],{"className":12338,"style":2478},[1850],[1788,12340,12342,12345],{"className":12341},[1844],[1788,12343,3101],{"className":12344,"style":3118},[1844,1845],[1788,12346,12348],{"className":12347},[1875],[1788,12349,12351,12371],{"className":12350},[1879,2931],[1788,12352,12354,12368],{"className":12353},[1883],[1788,12355,12357],{"className":12356,"style":2938},[1887],[1788,12358,12359,12362],{"style":9312},[1788,12360],{"className":12361,"style":1895},[1894],[1788,12363,12365],{"className":12364},[1899,1900,1901,1902],[1788,12366,2887],{"className":12367},[1844,1902],[1788,12369,2958],{"className":12370},[2957],[1788,12372,12374],{"className":12373},[1883],[1788,12375,12377],{"className":12376,"style":2965},[1887],[1788,12378],{},[1788,12380,2430],{"className":12381},[2474],[1788,12383],{"className":12384,"style":2478},[1850],[1788,12386,1987],{"className":12387},[1844],[1788,12389,1990],{"className":12390},[2079]," 能与 ",[1788,12393,12395,12433],{"className":12394},[1791],[1788,12396,12398],{"className":12397},[1795],[1797,12399,12400],{"xmlns":1799},[1801,12401,12402,12430],{},[1804,12403,12404,12406,12412,12414,12420,12422,12428],{},[1811,12405,1977],{"stretchy":1976},[2881,12407,12408,12410],{},[1807,12409,3101],{},[1985,12411,2906],{},[1811,12413,2430],{"separator":1831},[2881,12415,12416,12418],{},[1807,12417,3101],{},[1985,12419,2896],{},[1811,12421,2430],{"separator":1831},[2881,12423,12424,12426],{},[1807,12425,3101],{},[1985,12427,2887],{},[1811,12429,1990],{"stretchy":1976},[1823,12431,12432],{"encoding":1825},"(\\alpha_1,\\alpha_2,\\alpha_3)",[1788,12434,12436],{"className":12435,"ariaHidden":1831},[1830],[1788,12437,12439,12442,12445,12485,12488,12491,12531,12534,12537,12577],{"className":12438},[1835],[1788,12440],{"className":12441,"style":2003},[1839],[1788,12443,1977],{"className":12444},[2013],[1788,12446,12448,12451],{"className":12447},[1844],[1788,12449,3101],{"className":12450,"style":3118},[1844,1845],[1788,12452,12454],{"className":12453},[1875],[1788,12455,12457,12477],{"className":12456},[1879,2931],[1788,12458,12460,12474],{"className":12459},[1883],[1788,12461,12463],{"className":12462,"style":2938},[1887],[1788,12464,12465,12468],{"style":9312},[1788,12466],{"className":12467,"style":1895},[1894],[1788,12469,12471],{"className":12470},[1899,1900,1901,1902],[1788,12472,2906],{"className":12473},[1844,1902],[1788,12475,2958],{"className":12476},[2957],[1788,12478,12480],{"className":12479},[1883],[1788,12481,12483],{"className":12482,"style":2965},[1887],[1788,12484],{},[1788,12486,2430],{"className":12487},[2474],[1788,12489],{"className":12490,"style":2478},[1850],[1788,12492,12494,12497],{"className":12493},[1844],[1788,12495,3101],{"className":12496,"style":3118},[1844,1845],[1788,12498,12500],{"className":12499},[1875],[1788,12501,12503,12523],{"className":12502},[1879,2931],[1788,12504,12506,12520],{"className":12505},[1883],[1788,12507,12509],{"className":12508,"style":2938},[1887],[1788,12510,12511,12514],{"style":9312},[1788,12512],{"className":12513,"style":1895},[1894],[1788,12515,12517],{"className":12516},[1899,1900,1901,1902],[1788,12518,2896],{"className":12519},[1844,1902],[1788,12521,2958],{"className":12522},[2957],[1788,12524,12526],{"className":12525},[1883],[1788,12527,12529],{"className":12528,"style":2965},[1887],[1788,12530],{},[1788,12532,2430],{"className":12533},[2474],[1788,12535],{"className":12536,"style":2478},[1850],[1788,12538,12540,12543],{"className":12539},[1844],[1788,12541,3101],{"className":12542,"style":3118},[1844,1845],[1788,12544,12546],{"className":12545},[1875],[1788,12547,12549,12569],{"className":12548},[1879,2931],[1788,12550,12552,12566],{"className":12551},[1883],[1788,12553,12555],{"className":12554,"style":2938},[1887],[1788,12556,12557,12560],{"style":9312},[1788,12558],{"className":12559,"style":1895},[1894],[1788,12561,12563],{"className":12562},[1899,1900,1901,1902],[1788,12564,2887],{"className":12565},[1844,1902],[1788,12567,2958],{"className":12568},[2957],[1788,12570,12572],{"className":12571},[1883],[1788,12573,12575],{"className":12574,"style":2965},[1887],[1788,12576],{},[1788,12578,1990],{"className":12579},[2079]," 相互线性表示，但 ",[1788,12582,12584,12625],{"className":12583},[1791],[1788,12585,12587],{"className":12586},[1795],[1797,12588,12589],{"xmlns":1799},[1801,12590,12591,12623],{},[1804,12592,12593,12595,12601,12603,12609,12611,12617,12619,12621],{},[1811,12594,1977],{"stretchy":1976},[2881,12596,12597,12599],{},[1807,12598,3101],{},[1985,12600,2906],{},[1811,12602,2430],{"separator":1831},[2881,12604,12605,12607],{},[1807,12606,3101],{},[1985,12608,2896],{},[1811,12610,2430],{"separator":1831},[2881,12612,12613,12615],{},[1807,12614,3101],{},[1985,12616,2887],{},[1811,12618,2430],{"separator":1831},[1985,12620,1987],{},[1811,12622,1990],{"stretchy":1976},[1823,12624,12234],{"encoding":1825},[1788,12626,12628],{"className":12627,"ariaHidden":1831},[1830],[1788,12629,12631,12634,12637,12677,12680,12683,12723,12726,12729,12769,12772,12775,12778],{"className":12630},[1835],[1788,12632],{"className":12633,"style":2003},[1839],[1788,12635,1977],{"className":12636},[2013],[1788,12638,12640,12643],{"className":12639},[1844],[1788,12641,3101],{"className":12642,"style":3118},[1844,1845],[1788,12644,12646],{"className":12645},[1875],[1788,12647,12649,12669],{"className":12648},[1879,2931],[1788,12650,12652,12666],{"className":12651},[1883],[1788,12653,12655],{"className":12654,"style":2938},[1887],[1788,12656,12657,12660],{"style":9312},[1788,12658],{"className":12659,"style":1895},[1894],[1788,12661,12663],{"className":12662},[1899,1900,1901,1902],[1788,12664,2906],{"className":12665},[1844,1902],[1788,12667,2958],{"className":12668},[2957],[1788,12670,12672],{"className":12671},[1883],[1788,12673,12675],{"className":12674,"style":2965},[1887],[1788,12676],{},[1788,12678,2430],{"className":12679},[2474],[1788,12681],{"className":12682,"style":2478},[1850],[1788,12684,12686,12689],{"className":12685},[1844],[1788,12687,3101],{"className":12688,"style":3118},[1844,1845],[1788,12690,12692],{"className":12691},[1875],[1788,12693,12695,12715],{"className":12694},[1879,2931],[1788,12696,12698,12712],{"className":12697},[1883],[1788,12699,12701],{"className":12700,"style":2938},[1887],[1788,12702,12703,12706],{"style":9312},[1788,12704],{"className":12705,"style":1895},[1894],[1788,12707,12709],{"className":12708},[1899,1900,1901,1902],[1788,12710,2896],{"className":12711},[1844,1902],[1788,12713,2958],{"className":12714},[2957],[1788,12716,12718],{"className":12717},[1883],[1788,12719,12721],{"className":12720,"style":2965},[1887],[1788,12722],{},[1788,12724,2430],{"className":12725},[2474],[1788,12727],{"className":12728,"style":2478},[1850],[1788,12730,12732,12735],{"className":12731},[1844],[1788,12733,3101],{"className":12734,"style":3118},[1844,1845],[1788,12736,12738],{"className":12737},[1875],[1788,12739,12741,12761],{"className":12740},[1879,2931],[1788,12742,12744,12758],{"className":12743},[1883],[1788,12745,12747],{"className":12746,"style":2938},[1887],[1788,12748,12749,12752],{"style":9312},[1788,12750],{"className":12751,"style":1895},[1894],[1788,12753,12755],{"className":12754},[1899,1900,1901,1902],[1788,12756,2887],{"className":12757},[1844,1902],[1788,12759,2958],{"className":12760},[2957],[1788,12762,12764],{"className":12763},[1883],[1788,12765,12767],{"className":12766,"style":2965},[1887],[1788,12768],{},[1788,12770,2430],{"className":12771},[2474],[1788,12773],{"className":12774,"style":2478},[1850],[1788,12776,1987],{"className":12777},[1844],[1788,12779,1990],{"className":12780},[2079]," 不是 ",[1788,12783,12785,12805],{"className":12784},[1791],[1788,12786,12788],{"className":12787},[1795],[1797,12789,12790],{"xmlns":1799},[1801,12791,12792,12802],{},[1804,12793,12794,12796,12798,12800],{},[1807,12795,2290],{},[1807,12797,8230],{},[1811,12799,1813],{},[1985,12801,1987],{},[1823,12803,12804],{"encoding":1825},"Ax=0",[1788,12806,12808,12829],{"className":12807,"ariaHidden":1831},[1830],[1788,12809,12811,12814,12817,12820,12823,12826],{"className":12810},[1835],[1788,12812],{"className":12813,"style":1840},[1839],[1788,12815,2290],{"className":12816},[1844,1845],[1788,12818,8230],{"className":12819},[1844,1845],[1788,12821],{"className":12822,"style":1851},[1850],[1788,12824,1813],{"className":12825},[1855],[1788,12827],{"className":12828,"style":1851},[1850],[1788,12830,12832,12835],{"className":12831},[1835],[1788,12833],{"className":12834,"style":4209},[1839],[1788,12836,1987],{"className":12837},[1844]," 的基础解系。",[1096,12840,12841,12843,12844,12872,12873,12917],{},[1099,12842,11503],{}," 基础解系一定是线性无关的，但 B 选项 3 个向量是线性相关的（",[1788,12845,12847,12860],{"className":12846},[1791],[1788,12848,12850],{"className":12849},[1795],[1797,12851,12852],{"xmlns":1799},[1801,12853,12854,12858],{},[1804,12855,12856],{},[1985,12857,2887],{},[1823,12859,2887],{"encoding":1825},[1788,12861,12863],{"className":12862,"ariaHidden":1831},[1830],[1788,12864,12866,12869],{"className":12865},[1835],[1788,12867],{"className":12868,"style":4209},[1839],[1788,12870,2887],{"className":12871},[1844]," 个向量相加 ",[1788,12874,12876,12892],{"className":12875},[1791],[1788,12877,12879],{"className":12878},[1795],[1797,12880,12881],{"xmlns":1799},[1801,12882,12883,12889],{},[1804,12884,12885,12887],{},[1811,12886,1813],{},[1985,12888,1987],{},[1823,12890,12891],{"encoding":1825},"=0",[1788,12893,12895,12908],{"className":12894,"ariaHidden":1831},[1830],[1788,12896,12898,12902,12905],{"className":12897},[1835],[1788,12899],{"className":12900,"style":12901},[1839],"height:0.3669em;",[1788,12903,1813],{"className":12904},[1855],[1788,12906],{"className":12907,"style":1851},[1850],[1788,12909,12911,12914],{"className":12910},[1835],[1788,12912],{"className":12913,"style":4209},[1839],[1788,12915,1987],{"className":12916},[1844],"）。",[1096,12919,12920,12923,12924,8852,13048,13172,13173,8852,13296,13419],{},[1099,12921,12922],{},"C."," 像上面举的例子一样，",[1788,12925,12927,12953],{"className":12926},[1791],[1788,12928,12930],{"className":12929},[1795],[1797,12931,12932],{"xmlns":1799},[1801,12933,12934,12950],{},[1804,12935,12936,12942,12944],{},[2881,12937,12938,12940],{},[1807,12939,3101],{},[1985,12941,2906],{},[1811,12943,2430],{"separator":1831},[2881,12945,12946,12948],{},[1807,12947,3101],{},[1985,12949,2896],{},[1823,12951,12952],{"encoding":1825},"\\alpha_1,\\alpha_2",[1788,12954,12956],{"className":12955,"ariaHidden":1831},[1830],[1788,12957,12959,12962,13002,13005,13008],{"className":12958},[1835],[1788,12960],{"className":12961,"style":5356},[1839],[1788,12963,12965,12968],{"className":12964},[1844],[1788,12966,3101],{"className":12967,"style":3118},[1844,1845],[1788,12969,12971],{"className":12970},[1875],[1788,12972,12974,12994],{"className":12973},[1879,2931],[1788,12975,12977,12991],{"className":12976},[1883],[1788,12978,12980],{"className":12979,"style":2938},[1887],[1788,12981,12982,12985],{"style":9312},[1788,12983],{"className":12984,"style":1895},[1894],[1788,12986,12988],{"className":12987},[1899,1900,1901,1902],[1788,12989,2906],{"className":12990},[1844,1902],[1788,12992,2958],{"className":12993},[2957],[1788,12995,12997],{"className":12996},[1883],[1788,12998,13000],{"className":12999,"style":2965},[1887],[1788,13001],{},[1788,13003,2430],{"className":13004},[2474],[1788,13006],{"className":13007,"style":2478},[1850],[1788,13009,13011,13014],{"className":13010},[1844],[1788,13012,3101],{"className":13013,"style":3118},[1844,1845],[1788,13015,13017],{"className":13016},[1875],[1788,13018,13020,13040],{"className":13019},[1879,2931],[1788,13021,13023,13037],{"className":13022},[1883],[1788,13024,13026],{"className":13025,"style":2938},[1887],[1788,13027,13028,13031],{"style":9312},[1788,13029],{"className":13030,"style":1895},[1894],[1788,13032,13034],{"className":13033},[1899,1900,1901,1902],[1788,13035,2896],{"className":13036},[1844,1902],[1788,13038,2958],{"className":13039},[2957],[1788,13041,13043],{"className":13042},[1883],[1788,13044,13046],{"className":13045,"style":2965},[1887],[1788,13047],{},[1788,13049,13051,13077],{"className":13050},[1791],[1788,13052,13054],{"className":13053},[1795],[1797,13055,13056],{"xmlns":1799},[1801,13057,13058,13074],{},[1804,13059,13060,13066,13068],{},[2881,13061,13062,13064],{},[1807,13063,2850],{},[1985,13065,2906],{},[1811,13067,2430],{"separator":1831},[2881,13069,13070,13072],{},[1807,13071,2850],{},[1985,13073,2896],{},[1823,13075,13076],{"encoding":1825},"\\beta_1,\\beta_2",[1788,13078,13080],{"className":13079,"ariaHidden":1831},[1830],[1788,13081,13083,13086,13126,13129,13132],{"className":13082},[1835],[1788,13084],{"className":13085,"style":2041},[1839],[1788,13087,13089,13092],{"className":13088},[1844],[1788,13090,2850],{"className":13091,"style":2866},[1844,1845],[1788,13093,13095],{"className":13094},[1875],[1788,13096,13098,13118],{"className":13097},[1879,2931],[1788,13099,13101,13115],{"className":13100},[1883],[1788,13102,13104],{"className":13103,"style":2938},[1887],[1788,13105,13106,13109],{"style":2941},[1788,13107],{"className":13108,"style":1895},[1894],[1788,13110,13112],{"className":13111},[1899,1900,1901,1902],[1788,13113,2906],{"className":13114},[1844,1902],[1788,13116,2958],{"className":13117},[2957],[1788,13119,13121],{"className":13120},[1883],[1788,13122,13124],{"className":13123,"style":2965},[1887],[1788,13125],{},[1788,13127,2430],{"className":13128},[2474],[1788,13130],{"className":13131,"style":2478},[1850],[1788,13133,13135,13138],{"className":13134},[1844],[1788,13136,2850],{"className":13137,"style":2866},[1844,1845],[1788,13139,13141],{"className":13140},[1875],[1788,13142,13144,13164],{"className":13143},[1879,2931],[1788,13145,13147,13161],{"className":13146},[1883],[1788,13148,13150],{"className":13149,"style":2938},[1887],[1788,13151,13152,13155],{"style":2941},[1788,13153],{"className":13154,"style":1895},[1894],[1788,13156,13158],{"className":13157},[1899,1900,1901,1902],[1788,13159,2896],{"className":13160},[1844,1902],[1788,13162,2958],{"className":13163},[2957],[1788,13165,13167],{"className":13166},[1883],[1788,13168,13170],{"className":13169,"style":2965},[1887],[1788,13171],{}," 等秩，但是 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不能相互线性表示。",[1096,13421,13422],{},[1099,13423,11305],{},[1096,13425,13426],{},[2114,13427],{"alt":13428,"src":13429},"D选项","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1c58bf6.png",[1096,13431,3984,13432,13619,13620,8852,13808,13995],{},[1788,13433,13435,13472],{"className":13434},[1791],[1788,13436,13438],{"className":13437},[1795],[1797,13439,13440],{"xmlns":1799},[1801,13441,13442,13470],{},[1804,13443,13444,13446,13452,13454,13460,13462,13468],{},[1811,13445,1977],{"stretchy":1976},[2881,13447,13448,13450],{},[1807,13449,3101],{},[1985,13451,2906],{},[1811,13453,2430],{"separator":1831},[2881,13455,13456,13458],{},[1807,13457,3101],{},[1985,13459,2896],{},[1811,13461,2430],{"separator":1831},[2881,13463,13464,13466],{},[1807,13465,3101],{},[1985,13467,2887],{},[1811,13469,1990],{"stretchy":1976},[1823,13471,12432],{"encoding":1825},[1788,13473,13475],{"className":13474,"ariaHidden":1831},[1830],[1788,13476,13478,13481,13484,13524,13527,13530,13570,13573,13576,13616],{"className":13477},[1835],[1788,13479],{"className":13480,"style":2003},[1839],[1788,13482,1977],{"className":13483},[2013],[1788,13485,13487,13490],{"className":13486},[1844],[1788,13488,3101],{"className":13489,"style":3118},[1844,1845],[1788,13491,13493],{"className":13492},[1875],[1788,13494,13496,13516],{"className":13495},[1879,2931],[1788,13497,13499,13513],{"className":13498},[1883],[1788,13500,13502],{"className":13501,"style":2938},[1887],[1788,13503,13504,13507],{"style":9312},[1788,13505],{"className":13506,"style":1895},[1894],[1788,13508,13510],{"className":13509},[1899,1900,1901,1902],[1788,13511,2906],{"className":13512},[1844,1902],[1788,13514,2958],{"className":13515},[2957],[1788,13517,13519],{"className":13518},[1883],[1788,13520,13522],{"className":13521,"style":2965},[1887],[1788,13523],{},[1788,13525,2430],{"className":13526},[2474],[1788,13528],{"className":13529,"style":2478},[1850],[1788,13531,13533,13536],{"className":13532},[1844],[1788,13534,3101],{"className":13535,"style":3118},[1844,1845],[1788,13537,13539],{"className":13538},[1875],[1788,13540,13542,13562],{"className":13541},[1879,2931],[1788,13543,13545,13559],{"className":13544},[1883],[1788,13546,13548],{"className":13547,"style":2938},[1887],[1788,13549,13550,13553],{"style":9312},[1788,13551],{"className":13552,"style":1895},[1894],[1788,13554,13556],{"className":13555},[1899,1900,1901,1902],[1788,13557,2896],{"className":13558},[1844,1902],[1788,13560,2958],{"className":13561},[2957],[1788,13563,13565],{"className":13564},[1883],[1788,13566,13568],{"className":13567,"style":2965},[1887],[1788,13569],{},[1788,13571,2430],{"className":13572},[2474],[1788,13574],{"className":13575,"style":2478},[1850],[1788,13577,13579,13582],{"className":13578},[1844],[1788,13580,3101],{"className":13581,"style":3118},[1844,1845],[1788,13583,13585],{"className":13584},[1875],[1788,13586,13588,13608],{"className":13587},[1879,2931],[1788,13589,13591,13605],{"className":13590},[1883],[1788,13592,13594],{"className":13593,"style":2938},[1887],[1788,13595,13596,13599],{"style":9312},[1788,13597],{"className":13598,"style":1895},[1894],[1788,13600,13602],{"className":13601},[1899,1900,1901,1902],[1788,13603,2887],{"className":13604},[1844,1902],[1788,13606,2958],{"className":13607},[2957],[1788,13609,13611],{"className":13610},[1883],[1788,13612,13614],{"className":13613,"style":2965},[1887],[1788,13615],{},[1788,13617,1990],{"className":13618},[2079]," 的右边乘可逆矩阵，不改变原来矩阵的秩，且 ",[1788,13621,13623,13661],{"className":13622},[1791],[1788,13624,13626],{"className":13625},[1795],[1797,13627,13628],{"xmlns":1799},[1801,13629,13630,13658],{},[1804,13631,13632,13634,13640,13642,13648,13650,13656],{},[1811,13633,1977],{"stretchy":1976},[2881,13635,13636,13638],{},[1807,13637,2850],{},[1985,13639,2906],{},[1811,13641,2430],{"separator":1831},[2881,13643,13644,13646],{},[1807,13645,2850],{},[1985,13647,2896],{},[1811,13649,2430],{"separator":1831},[2881,13651,13652,13654],{},[1807,13653,2850],{},[1985,13655,2887],{},[1811,13657,1990],{"stretchy":1976},[1823,13659,13660],{"encoding":1825},"(\\beta_1,\\beta_2,\\beta_3)",[1788,13662,13664],{"className":13663,"ariaHidden":1831},[1830],[1788,13665,13667,13670,13673,13713,13716,13719,13759,13762,13765,13805],{"className":13666},[1835],[1788,13668],{"className":13669,"style":2003},[1839],[1788,13671,1977],{"className":13672},[2013],[1788,13674,13676,13679],{"className":13675},[1844],[1788,13677,2850],{"className":13678,"style":2866},[1844,1845],[1788,13680,13682],{"className":13681},[1875],[1788,13683,13685,13705],{"className":13684},[1879,2931],[1788,13686,13688,13702],{"className":13687},[1883],[1788,13689,13691],{"className":13690,"style":2938},[1887],[1788,13692,13693,13696],{"style":2941},[1788,13694],{"className":13695,"style":1895},[1894],[1788,13697,13699],{"className":13698},[1899,1900,1901,1902],[1788,13700,2906],{"className":13701},[1844,1902],[1788,13703,2958],{"className":13704},[2957],[1788,13706,13708],{"className":13707},[1883],[1788,13709,13711],{"className":13710,"style":2965},[1887],[1788,13712],{},[1788,13714,2430],{"className":13715},[2474],[1788,13717],{"className":13718,"style":2478},[1850],[1788,13720,13722,13725],{"className":13721},[1844],[1788,13723,2850],{"className":13724,"style":2866},[1844,1845],[1788,13726,13728],{"className":13727},[1875],[1788,13729,13731,13751],{"className":13730},[1879,2931],[1788,13732,13734,13748],{"className":13733},[1883],[1788,13735,13737],{"className":13736,"style":2938},[1887],[1788,13738,13739,13742],{"style":2941},[1788,13740],{"className":13741,"style":1895},[1894],[1788,13743,13745],{"className":13744},[1899,1900,1901,1902],[1788,13746,2896],{"className":13747},[1844,1902],[1788,13749,2958],{"className":13750},[2957],[1788,13752,13754],{"className":13753},[1883],[1788,13755,13757],{"className":13756,"style":2965},[1887],[1788,13758],{},[1788,13760,2430],{"className":13761},[2474],[1788,13763],{"className":13764,"style":2478},[1850],[1788,13766,13768,13771],{"className":13767},[1844],[1788,13769,2850],{"className":13770,"style":2866},[1844,1845],[1788,13772,13774],{"className":13773},[1875],[1788,13775,13777,13797],{"className":13776},[1879,2931],[1788,13778,13780,13794],{"className":13779},[1883],[1788,13781,13783],{"className":13782,"style":2938},[1887],[1788,13784,13785,13788],{"style":2941},[1788,13786],{"className":13787,"style":1895},[1894],[1788,13789,13791],{"className":13790},[1899,1900,1901,1902],[1788,13792,2887],{"className":13793},[1844,1902],[1788,13795,2958],{"className":13796},[2957],[1788,13798,13800],{"className":13799},[1883],[1788,13801,13803],{"className":13802,"style":2965},[1887],[1788,13804],{},[1788,13806,1990],{"className":13807},[2079],[1788,13809,13811,13848],{"className":13810},[1791],[1788,13812,13814],{"className":13813},[1795],[1797,13815,13816],{"xmlns":1799},[1801,13817,13818,13846],{},[1804,13819,13820,13822,13828,13830,13836,13838,13844],{},[1811,13821,1977],{"stretchy":1976},[2881,13823,13824,13826],{},[1807,13825,3101],{},[1985,13827,2906],{},[1811,13829,2430],{"separator":1831},[2881,13831,13832,13834],{},[1807,13833,3101],{},[1985,13835,2896],{},[1811,13837,2430],{"separator":1831},[2881,13839,13840,13842],{},[1807,13841,3101],{},[1985,13843,2887],{},[1811,13845,1990],{"stretchy":1976},[1823,13847,12432],{"encoding":1825},[1788,13849,13851],{"className":13850,"ariaHidden":1831},[1830],[1788,13852,13854,13857,13860,13900,13903,13906,13946,13949,13952,13992],{"className":13853},[1835],[1788,13855],{"className":13856,"style":2003},[1839],[1788,13858,1977],{"className":13859},[2013],[1788,13861,13863,13866],{"className":13862},[1844],[1788,13864,3101],{"className":13865,"style":3118},[1844,1845],[1788,13867,13869],{"className":13868},[1875],[1788,13870,13872,13892],{"className":13871},[1879,2931],[1788,13873,13875,13889],{"className":13874},[1883],[1788,13876,13878],{"className":13877,"style":2938},[1887],[1788,13879,13880,13883],{"style":9312},[1788,13881],{"className":13882,"style":1895},[1894],[1788,13884,13886],{"className":13885},[1899,1900,1901,1902],[1788,13887,2906],{"className":13888},[1844,1902],[1788,13890,2958],{"className":13891},[2957],[1788,13893,13895],{"className":13894},[1883],[1788,13896,13898],{"className":13897,"style":2965},[1887],[1788,13899],{},[1788,13901,2430],{"className":13902},[2474],[1788,13904],{"className":13905,"style":2478},[1850],[1788,13907,13909,13912],{"className":13908},[1844],[1788,13910,3101],{"className":13911,"style":3118},[1844,1845],[1788,13913,13915],{"className":13914},[1875],[1788,13916,13918,13938],{"className":13917},[1879,2931],[1788,13919,13921,13935],{"className":13920},[1883],[1788,13922,13924],{"className":13923,"style":2938},[1887],[1788,13925,13926,13929],{"style":9312},[1788,13927],{"className":13928,"style":1895},[1894],[1788,13930,13932],{"className":13931},[1899,1900,1901,1902],[1788,13933,2896],{"className":13934},[1844,1902],[1788,13936,2958],{"className":13937},[2957],[1788,13939,13941],{"className":13940},[1883],[1788,13942,13944],{"className":13943,"style":2965},[1887],[1788,13945],{},[1788,13947,2430],{"className":13948},[2474],[1788,13950],{"className":13951,"style":2478},[1850],[1788,13953,13955,13958],{"className":13954},[1844],[1788,13956,3101],{"className":13957,"style":3118},[1844,1845],[1788,13959,13961],{"className":13960},[1875],[1788,13962,13964,13984],{"className":13963},[1879,2931],[1788,13965,13967,13981],{"className":13966},[1883],[1788,13968,13970],{"className":13969,"style":2938},[1887],[1788,13971,13972,13975],{"style":9312},[1788,13973],{"className":13974,"style":1895},[1894],[1788,13976,13978],{"className":13977},[1899,1900,1901,1902],[1788,13979,2887],{"className":13980},[1844,1902],[1788,13982,2958],{"className":13983},[2957],[1788,13985,13987],{"className":13986},[1883],[1788,13988,13990],{"className":13989,"style":2965},[1887],[1788,13991],{},[1788,13993,1990],{"className":13994},[2079]," 能相互线性表示。",[1096,13997,13998],{},[1099,13999,14000,14001,14056],{},"所以，求 ",[1788,14002,14004,14023],{"className":14003},[1791],[1788,14005,14007],{"className":14006},[1795],[1797,14008,14009],{"xmlns":1799},[1801,14010,14011,14021],{},[1804,14012,14013,14015,14017,14019],{},[1807,14014,2290],{},[1807,14016,8230],{},[1811,14018,1813],{},[1985,14020,1987],{},[1823,14022,12804],{"encoding":1825},[1788,14024,14026,14047],{"className":14025,"ariaHidden":1831},[1830],[1788,14027,14029,14032,14035,14038,14041,14044],{"className":14028},[1835],[1788,14030],{"className":14031,"style":1840},[1839],[1788,14033,2290],{"className":14034},[1844,1845],[1788,14036,8230],{"className":14037},[1844,1845],[1788,14039],{"className":14040,"style":1851},[1850],[1788,14042,1813],{"className":14043},[1855],[1788,14045],{"className":14046,"style":1851},[1850],[1788,14048,14050,14053],{"className":14049},[1835],[1788,14051],{"className":14052,"style":4209},[1839],[1788,14054,1987],{"className":14055},[1844]," 的另一个基础解系，需要满足其等价且等秩。",[1780,14058,14060],{"id":14059},"_4-同解方程组","4. 同解方程组",[1096,14062,14063,14064,8852,14176,14288],{},"若两个方程组 ",[1788,14065,14067,14097],{"className":14066},[1791],[1788,14068,14070],{"className":14069},[1795],[1797,14071,14072],{"xmlns":1799},[1801,14073,14074,14094],{},[1804,14075,14076,14088,14090,14092],{},[2881,14077,14078,14080],{},[1807,14079,2290],{},[1804,14081,14082,14084,14086],{},[1807,14083,4911],{},[1811,14085,4914],{},[1807,14087,2301],{},[1807,14089,8230],{},[1811,14091,1813],{},[1985,14093,1987],{},[1823,14095,14096],{"encoding":1825},"A_{m\\times n}x=0",[1788,14098,14100,14167],{"className":14099,"ariaHidden":1831},[1830],[1788,14101,14103,14106,14155,14158,14161,14164],{"className":14102},[1835],[1788,14104],{"className":14105,"style":7282},[1839],[1788,14107,14109,14112],{"className":14108},[1844],[1788,14110,2290],{"className":14111},[1844,1845],[1788,14113,14115],{"className":14114},[1875],[1788,14116,14118,14147],{"className":14117},[1879,2931],[1788,14119,14121,14144],{"className":14120},[1883],[1788,14122,14124],{"className":14123,"style":7301},[1887],[1788,14125,14126,14129],{"style":4072},[1788,14127],{"className":14128,"style":1895},[1894],[1788,14130,14132],{"className":14131},[1899,1900,1901,1902],[1788,14133,14135,14138,14141],{"className":14134},[1844,1902],[1788,14136,4911],{"className":14137},[1844,1845,1902],[1788,14139,4914],{"className":14140},[3033,1902],[1788,14142,2301],{"className":14143},[1844,1845,1902],[1788,14145,2958],{"className":14146},[2957],[1788,14148,14150],{"className":14149},[1883],[1788,14151,14153],{"className":14152,"style":7331},[1887],[1788,14154],{},[1788,14156,8230],{"className":14157},[1844,1845],[1788,14159],{"className":14160,"style":1851},[1850],[1788,14162,1813],{"className":14163},[1855],[1788,14165],{"className":14166,"style":1851},[1850],[1788,14168,14170,14173],{"className":14169},[1835],[1788,14171],{"className":14172,"style":4209},[1839],[1788,14174,1987],{"className":14175},[1844],[1788,14177,14179,14209],{"className":14178},[1791],[1788,14180,14182],{"className":14181},[1795],[1797,14183,14184],{"xmlns":1799},[1801,14185,14186,14206],{},[1804,14187,14188,14200,14202,14204],{},[2881,14189,14190,14192],{},[1807,14191,3841],{},[1804,14193,14194,14196,14198],{},[1807,14195,7264],{},[1811,14197,4914],{},[1807,14199,2301],{},[1807,14201,8230],{},[1811,14203,1813],{},[1985,14205,1987],{},[1823,14207,14208],{"encoding":1825},"B_{s\\times n}x=0",[1788,14210,14212,14279],{"className":14211,"ariaHidden":1831},[1830],[1788,14213,14215,14218,14267,14270,14273,14276],{"className":14214},[1835],[1788,14216],{"className":14217,"style":7282},[1839],[1788,14219,14221,14224],{"className":14220},[1844],[1788,14222,3841],{"className":14223,"style":3866},[1844,1845],[1788,14225,14227],{"className":14226},[1875],[1788,14228,14230,14259],{"className":14229},[1879,2931],[1788,14231,14233,14256],{"className":14232},[1883],[1788,14234,14236],{"className":14235,"style":7301},[1887],[1788,14237,14238,14241],{"style":7354},[1788,14239],{"className":14240,"style":1895},[1894],[1788,14242,14244],{"className":14243},[1899,1900,1901,1902],[1788,14245,14247,14250,14253],{"className":14246},[1844,1902],[1788,14248,7264],{"className":14249},[1844,1845,1902],[1788,14251,4914],{"className":14252},[3033,1902],[1788,14254,2301],{"className":14255},[1844,1845,1902],[1788,14257,2958],{"className":14258},[2957],[1788,14260,14262],{"className":14261},[1883],[1788,14263,14265],{"className":14264,"style":7331},[1887],[1788,14266],{},[1788,14268,8230],{"className":14269},[1844,1845],[1788,14271],{"className":14272,"style":1851},[1850],[1788,14274,1813],{"className":14275},[1855],[1788,14277],{"className":14278,"style":1851},[1850],[1788,14280,14282,14285],{"className":14281},[1835],[1788,14283],{"className":14284,"style":4209},[1839],[1788,14286,1987],{"className":14287},[1844]," 有完全相同的解，则称它们为同解方程组。",[1912,14290,14291,14296],{},[1096,14292,14293],{},[1099,14294,14295],{},"充要条件：",[1096,14297,6300,14298,14353,14354,9890,14410,14353,14465,14520,14521,9890,14601,14353,14656,14711,14712,14353,14767,14822,14823,14963],{},[1788,14299,14301,14320],{"className":14300},[1791],[1788,14302,14304],{"className":14303},[1795],[1797,14305,14306],{"xmlns":1799},[1801,14307,14308,14318],{},[1804,14309,14310,14312,14314,14316],{},[1807,14311,2290],{},[1807,14313,8230],{},[1811,14315,1813],{},[1985,14317,1987],{},[1823,14319,12804],{"encoding":1825},[1788,14321,14323,14344],{"className":14322,"ariaHidden":1831},[1830],[1788,14324,14326,14329,14332,14335,14338,14341],{"className":14325},[1835],[1788,14327],{"className":14328,"style":1840},[1839],[1788,14330,2290],{"className":14331},[1844,1845],[1788,14333,8230],{"className":14334},[1844,1845],[1788,14336],{"className":14337,"style":1851},[1850],[1788,14339,1813],{"className":14340},[1855],[1788,14342],{"className":14343,"style":1851},[1850],[1788,14345,14347,14350],{"className":14346},[1835],[1788,14348],{"className":14349,"style":4209},[1839],[1788,14351,1987],{"className":14352},[1844]," 的解满足 ",[1788,14355,14357,14377],{"className":14356},[1791],[1788,14358,14360],{"className":14359},[1795],[1797,14361,14362],{"xmlns":1799},[1801,14363,14364,14374],{},[1804,14365,14366,14368,14370,14372],{},[1807,14367,3841],{},[1807,14369,8230],{},[1811,14371,1813],{},[1985,14373,1987],{},[1823,14375,14376],{"encoding":1825},"Bx=0",[1788,14378,14380,14401],{"className":14379,"ariaHidden":1831},[1830],[1788,14381,14383,14386,14389,14392,14395,14398],{"className":14382},[1835],[1788,14384],{"className":14385,"style":1840},[1839],[1788,14387,3841],{"className":14388,"style":3866},[1844,1845],[1788,14390,8230],{"className":14391},[1844,1845],[1788,14393],{"className":14394,"style":1851},[1850],[1788,14396,1813],{"className":14397},[1855],[1788,14399],{"className":14400,"style":1851},[1850],[1788,14402,14404,14407],{"className":14403},[1835],[1788,14405],{"className":14406,"style":4209},[1839],[1788,14408,1987],{"className":14409},[1844],[1788,14411,14413,14432],{"className":14412},[1791],[1788,14414,14416],{"className":14415},[1795],[1797,14417,14418],{"xmlns":1799},[1801,14419,14420,14430],{},[1804,14421,14422,14424,14426,14428],{},[1807,14423,3841],{},[1807,14425,8230],{},[1811,14427,1813],{},[1985,14429,1987],{},[1823,14431,14376],{"encoding":1825},[1788,14433,14435,14456],{"className":14434,"ariaHidden":1831},[1830],[1788,14436,14438,14441,14444,14447,14450,14453],{"className":14437},[1835],[1788,14439],{"className":14440,"style":1840},[1839],[1788,14442,3841],{"className":14443,"style":3866},[1844,1845],[1788,14445,8230],{"className":14446},[1844,1845],[1788,14448],{"className":14449,"style":1851},[1850],[1788,14451,1813],{"className":14452},[1855],[1788,14454],{"className":14455,"style":1851},[1850],[1788,14457,14459,14462],{"className":14458},[1835],[1788,14460],{"className":14461,"style":4209},[1839],[1788,14463,1987],{"className":14464},[1844],[1788,14466,14468,14487],{"className":14467},[1791],[1788,14469,14471],{"className":14470},[1795],[1797,14472,14473],{"xmlns":1799},[1801,14474,14475,14485],{},[1804,14476,14477,14479,14481,14483],{},[1807,14478,2290],{},[1807,14480,8230],{},[1811,14482,1813],{},[1985,14484,1987],{},[1823,14486,12804],{"encoding":1825},[1788,14488,14490,14511],{"className":14489,"ariaHidden":1831},[1830],[1788,14491,14493,14496,14499,14502,14505,14508],{"className":14492},[1835],[1788,14494],{"className":14495,"style":1840},[1839],[1788,14497,2290],{"className":14498},[1844,1845],[1788,14500,8230],{"className":14501},[1844,1845],[1788,14503],{"className":14504,"style":1851},[1850],[1788,14506,1813],{"className":14507},[1855],[1788,14509],{"className":14510,"style":1851},[1850],[1788,14512,14514,14517],{"className":14513},[1835],[1788,14515],{"className":14516,"style":4209},[1839],[1788,14518,1987],{"className":14519},[1844],"（互相把解代入求出结果即可）\n② ",[1788,14522,14524,14553],{"className":14523},[1791],[1788,14525,14527],{"className":14526},[1795],[1797,14528,14529],{"xmlns":1799},[1801,14530,14531,14551],{},[1804,14532,14533,14535,14537,14539,14541,14543,14545,14547,14549],{},[1807,14534,2421],{},[1811,14536,1977],{"stretchy":1976},[1807,14538,2290],{},[1811,14540,1990],{"stretchy":1976},[1811,14542,1813],{},[1807,14544,2421],{},[1811,14546,1977],{"stretchy":1976},[1807,14548,3841],{},[1811,14550,1990],{"stretchy":1976},[1823,14552,8970],{"encoding":1825},[1788,14554,14556,14583],{"className":14555,"ariaHidden":1831},[1830],[1788,14557,14559,14562,14565,14568,14571,14574,14577,14580],{"className":14558},[1835],[1788,14560],{"className":14561,"style":2003},[1839],[1788,14563,2421],{"className":14564,"style":1846},[1844,1845],[1788,14566,1977],{"className":14567},[2013],[1788,14569,2290],{"className":14570},[1844,1845],[1788,14572,1990],{"className":14573},[2079],[1788,14575],{"className":14576,"style":1851},[1850],[1788,14578,1813],{"className":14579},[1855],[1788,14581],{"className":14582,"style":1851},[1850],[1788,14584,14586,14589,14592,14595,14598],{"className":14585},[1835],[1788,14587],{"className":14588,"style":2003},[1839],[1788,14590,2421],{"className":14591,"style":1846},[1844,1845],[1788,14593,1977],{"className":14594},[2013],[1788,14596,3841],{"className":14597,"style":3866},[1844,1845],[1788,14599,1990],{"className":14600},[2079],[1788,14602,14604,14623],{"className":14603},[1791],[1788,14605,14607],{"className":14606},[1795],[1797,14608,14609],{"xmlns":1799},[1801,14610,14611,14621],{},[1804,14612,14613,14615,14617,14619],{},[1807,14614,2290],{},[1807,14616,8230],{},[1811,14618,1813],{},[1985,14620,1987],{},[1823,14622,12804],{"encoding":1825},[1788,14624,14626,14647],{"className":14625,"ariaHidden":1831},[1830],[1788,14627,14629,14632,14635,14638,14641,14644],{"className":14628},[1835],[1788,14630],{"className":14631,"style":1840},[1839],[1788,14633,2290],{"className":14634},[1844,1845],[1788,14636,8230],{"className":14637},[1844,1845],[1788,14639],{"className":14640,"style":1851},[1850],[1788,14642,1813],{"className":14643},[1855],[1788,14645],{"className":14646,"style":1851},[1850],[1788,14648,14650,14653],{"className":14649},[1835],[1788,14651],{"className":14652,"style":4209},[1839],[1788,14654,1987],{"className":14655},[1844],[1788,14657,14659,14678],{"className":14658},[1791],[1788,14660,14662],{"className":14661},[1795],[1797,14663,14664],{"xmlns":1799},[1801,14665,14666,14676],{},[1804,14667,14668,14670,14672,14674],{},[1807,14669,3841],{},[1807,14671,8230],{},[1811,14673,1813],{},[1985,14675,1987],{},[1823,14677,14376],{"encoding":1825},[1788,14679,14681,14702],{"className":14680,"ariaHidden":1831},[1830],[1788,14682,14684,14687,14690,14693,14696,14699],{"className":14683},[1835],[1788,14685],{"className":14686,"style":1840},[1839],[1788,14688,3841],{"className":14689,"style":3866},[1844,1845],[1788,14691,8230],{"className":14692},[1844,1845],[1788,14694],{"className":14695,"style":1851},[1850],[1788,14697,1813],{"className":14698},[1855],[1788,14700],{"className":14701,"style":1851},[1850],[1788,14703,14705,14708],{"className":14704},[1835],[1788,14706],{"className":14707,"style":4209},[1839],[1788,14709,1987],{"className":14710},[1844],"（或 ",[1788,14713,14715,14734],{"className":14714},[1791],[1788,14716,14718],{"className":14717},[1795],[1797,14719,14720],{"xmlns":1799},[1801,14721,14722,14732],{},[1804,14723,14724,14726,14728,14730],{},[1807,14725,3841],{},[1807,14727,8230],{},[1811,14729,1813],{},[1985,14731,1987],{},[1823,14733,14376],{"encoding":1825},[1788,14735,14737,14758],{"className":14736,"ariaHidden":1831},[1830],[1788,14738,14740,14743,14746,14749,14752,14755],{"className":14739},[1835],[1788,14741],{"className":14742,"style":1840},[1839],[1788,14744,3841],{"className":14745,"style":3866},[1844,1845],[1788,14747,8230],{"className":14748},[1844,1845],[1788,14750],{"className":14751,"style":1851},[1850],[1788,14753,1813],{"className":14754},[1855],[1788,14756],{"className":14757,"style":1851},[1850],[1788,14759,14761,14764],{"className":14760},[1835],[1788,14762],{"className":14763,"style":4209},[1839],[1788,14765,1987],{"className":14766},[1844],[1788,14768,14770,14789],{"className":14769},[1791],[1788,14771,14773],{"className":14772},[1795],[1797,14774,14775],{"xmlns":1799},[1801,14776,14777,14787],{},[1804,14778,14779,14781,14783,14785],{},[1807,14780,2290],{},[1807,14782,8230],{},[1811,14784,1813],{},[1985,14786,1987],{},[1823,14788,12804],{"encoding":1825},[1788,14790,14792,14813],{"className":14791,"ariaHidden":1831},[1830],[1788,14793,14795,14798,14801,14804,14807,14810],{"className":14794},[1835],[1788,14796],{"className":14797,"style":1840},[1839],[1788,14799,2290],{"className":14800},[1844,1845],[1788,14802,8230],{"className":14803},[1844,1845],[1788,14805],{"className":14806,"style":1851},[1850],[1788,14808,1813],{"className":14809},[1855],[1788,14811],{"className":14812,"style":1851},[1850],[1788,14814,14816,14819],{"className":14815},[1835],[1788,14817],{"className":14818,"style":4209},[1839],[1788,14820,1987],{"className":14821},[1844],"）\n③ ",[1788,14824,14826,14877],{"className":14825},[1791],[1788,14827,14829],{"className":14828},[1795],[1797,14830,14831],{"xmlns":1799},[1801,14832,14833,14874],{},[1804,14834,14835,14837,14839,14841,14843,14845,14847,14849,14851,14853,14855,14857,14859,14862,14864,14867,14869,14872],{},[1807,14836,2421],{},[1811,14838,1977],{"stretchy":1976},[1807,14840,2290],{},[1811,14842,1990],{"stretchy":1976},[1811,14844,1813],{},[1807,14846,2421],{},[1811,14848,1977],{"stretchy":1976},[1807,14850,3841],{},[1811,14852,1990],{"stretchy":1976},[1811,14854,1813],{},[1807,14856,2421],{},[1811,14858,1977],{"stretchy":1976},[1811,14860,14861],{"stretchy":1976},"[",[1807,14863,2290],{},[1811,14865,14866],{"separator":1831},";",[1807,14868,3841],{},[1811,14870,14871],{"stretchy":1976},"]",[1811,14873,1990],{"stretchy":1976},[1823,14875,14876],{"encoding":1825},"r(A)=r(B)=r([A;B])",[1788,14878,14880,14907,14934],{"className":14879,"ariaHidden":1831},[1830],[1788,14881,14883,14886,14889,14892,14895,14898,14901,14904],{"className":14882},[1835],[1788,14884],{"className":14885,"style":2003},[1839],[1788,14887,2421],{"className":14888,"style":1846},[1844,1845],[1788,14890,1977],{"className":14891},[2013],[1788,14893,2290],{"className":14894},[1844,1845],[1788,14896,1990],{"className":14897},[2079],[1788,14899],{"className":14900,"style":1851},[1850],[1788,14902,1813],{"className":14903},[1855],[1788,14905],{"className":14906,"style":1851},[1850],[1788,14908,14910,14913,14916,14919,14922,14925,14928,14931],{"className":14909},[1835],[1788,14911],{"className":14912,"style":2003},[1839],[1788,14914,2421],{"className":14915,"style":1846},[1844,1845],[1788,14917,1977],{"className":14918},[2013],[1788,14920,3841],{"className":14921,"style":3866},[1844,1845],[1788,14923,1990],{"className":14924},[2079],[1788,14926],{"className":14927,"style":1851},[1850],[1788,14929,1813],{"className":14930},[1855],[1788,14932],{"className":14933,"style":1851},[1850],[1788,14935,14937,14940,14943,14947,14950,14953,14956,14959],{"className":14936},[1835],[1788,14938],{"className":14939,"style":2003},[1839],[1788,14941,2421],{"className":14942,"style":1846},[1844,1845],[1788,14944,14946],{"className":14945},[2013],"([",[1788,14948,2290],{"className":14949},[1844,1845],[1788,14951,14866],{"className":14952},[2474],[1788,14954],{"className":14955,"style":2478},[1850],[1788,14957,3841],{"className":14958,"style":3866},[1844,1845],[1788,14960,14962],{"className":14961},[2079],"])","（三秩相同）",[1096,14965,14966],{},[1099,14967,14968],{},"例1：",[1096,14970,14971],{},[2114,14972],{"alt":14973,"src":14974},"同解方程组例1","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1c67ad1.png",[1096,14976,14977],{},[1099,14978,14979],{},"例2：",[1096,14981,14982],{},[2114,14983],{"alt":14984,"src":14985},"同解方程组例2","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1da3ebf.png",[1096,14987,14988],{},[1099,14989,14990],{},"例3：",[1096,14992,14993],{},[2114,14994],{"alt":14995,"src":14996},"同解方程组例3","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1da5b0a.png",[1091,14998,15000],{"id":14999},"七-齐次线性方程组和非齐次线性方程组","七. 齐次线性方程组和非齐次线性方程组",[1912,15002,15003,15008,15224,15748,15754],{},[1096,15004,15005],{},[1099,15006,15007],{},"齐次线性方程组有解的条件：",[1096,15009,6300,15010,15076,15077,15080,15081,15171,15172,15223],{},[1788,15011,15013,15037],{"className":15012},[1791],[1788,15014,15016],{"className":15015},[1795],[1797,15017,15018],{"xmlns":1799},[1801,15019,15020,15034],{},[1804,15021,15022,15024,15026,15028,15030,15032],{},[1807,15023,2421],{},[1811,15025,1977],{"stretchy":1976},[1807,15027,2290],{},[1811,15029,1990],{"stretchy":1976},[1811,15031,1813],{},[1807,15033,2301],{},[1823,15035,15036],{"encoding":1825},"r(A)=n",[1788,15038,15040,15067],{"className":15039,"ariaHidden":1831},[1830],[1788,15041,15043,15046,15049,15052,15055,15058,15061,15064],{"className":15042},[1835],[1788,15044],{"className":15045,"style":2003},[1839],[1788,15047,2421],{"className":15048,"style":1846},[1844,1845],[1788,15050,1977],{"className":15051},[2013],[1788,15053,2290],{"className":15054},[1844,1845],[1788,15056,1990],{"className":15057},[2079],[1788,15059],{"className":15060,"style":1851},[1850],[1788,15062,1813],{"className":15063},[1855],[1788,15065],{"className":15066,"style":1851},[1850],[1788,15068,15070,15073],{"className":15069},[1835],[1788,15071],{"className":15072,"style":3114},[1839],[1788,15074,2301],{"className":15075},[1844,1845]," 时，方程组有",[1099,15078,15079],{},"唯一零解","。\n② ",[1788,15082,15084,15113],{"className":15083},[1791],[1788,15085,15087],{"className":15086},[1795],[1797,15088,15089],{"xmlns":1799},[1801,15090,15091,15110],{},[1804,15092,15093,15095,15097,15099,15101,15103,15105,15108],{},[1807,15094,2421],{},[1811,15096,1977],{"stretchy":1976},[1807,15098,2290],{},[1811,15100,1990],{"stretchy":1976},[1811,15102,1813],{},[1807,15104,2421],{},[1811,15106,15107],{},"\u003C",[1807,15109,2301],{},[1823,15111,15112],{"encoding":1825},"r(A)=r\u003Cn",[1788,15114,15116,15143,15162],{"className":15115,"ariaHidden":1831},[1830],[1788,15117,15119,15122,15125,15128,15131,15134,15137,15140],{"className":15118},[1835],[1788,15120],{"className":15121,"style":2003},[1839],[1788,15123,2421],{"className":15124,"style":1846},[1844,1845],[1788,15126,1977],{"className":15127},[2013],[1788,15129,2290],{"className":15130},[1844,1845],[1788,15132,1990],{"className":15133},[2079],[1788,15135],{"className":15136,"style":1851},[1850],[1788,15138,1813],{"className":15139},[1855],[1788,15141],{"className":15142,"style":1851},[1850],[1788,15144,15146,15150,15153,15156,15159],{"className":15145},[1835],[1788,15147],{"className":15148,"style":15149},[1839],"height:0.5782em;vertical-align:-0.0391em;",[1788,15151,2421],{"className":15152,"style":1846},[1844,1845],[1788,15154],{"className":15155,"style":1851},[1850],[1788,15157,15107],{"className":15158},[1855],[1788,15160],{"className":15161,"style":1851},[1850],[1788,15163,15165,15168],{"className":15164},[1835],[1788,15166],{"className":15167,"style":3114},[1839],[1788,15169,2301],{"className":15170},[1844,1845]," 时，方程组有非零解（无穷多解），且有 ",[1788,15173,15175,15193],{"className":15174},[1791],[1788,15176,15178],{"className":15177},[1795],[1797,15179,15180],{"xmlns":1799},[1801,15181,15182,15190],{},[1804,15183,15184,15186,15188],{},[1807,15185,2301],{},[1811,15187,3250],{},[1807,15189,2421],{},[1823,15191,15192],{"encoding":1825},"n-r",[1788,15194,15196,15214],{"className":15195,"ariaHidden":1831},[1830],[1788,15197,15199,15202,15205,15208,15211],{"className":15198},[1835],[1788,15200],{"className":15201,"style":4190},[1839],[1788,15203,2301],{"className":15204},[1844,1845],[1788,15206],{"className":15207,"style":3029},[1850],[1788,15209,3250],{"className":15210},[3033],[1788,15212],{"className":15213,"style":3029},[1850],[1788,15215,15217,15220],{"className":15216},[1835],[1788,15218],{"className":15219,"style":3114},[1839],[1788,15221,2421],{"className":15222,"style":1846},[1844,1845]," 个线性无关解。",[1096,15225,15226,15229,15230],{},[1099,15227,15228],{},"齐次方程组其实就是解和系数的正交","，例如，给你一个条件：\n",[1788,15231,15233,15317],{"className":15232},[1791],[1788,15234,15236],{"className":15235},[1795],[1797,15237,15238],{"xmlns":1799},[1801,15239,15240,15314],{},[1804,15241,15242,15248,15250,15252,15258,15260,15266,15268,15271,15273,15279,15281,15283,15289,15291,15297,15299,15301,15304,15310,15312],{},[2881,15243,15244,15246],{},[1807,15245,3101],{},[1985,15247,2906],{},[1811,15249,1813],{},[1985,15251,2896],{},[2881,15253,15254,15256],{},[1807,15255,3101],{},[1985,15257,2896],{},[1811,15259,2899],{},[2881,15261,15262,15264],{},[1807,15263,3101],{},[1985,15265,2887],{},[1971,15267,1973],{},[1811,15269,15270],{},"⟹",[1971,15272,1973],{},[2881,15274,15275,15277],{},[1807,15276,3101],{},[1985,15278,2906],{},[1811,15280,3250],{},[1985,15282,2896],{},[2881,15284,15285,15287],{},[1807,15286,3101],{},[1985,15288,2896],{},[1811,15290,3250],{},[2881,15292,15293,15295],{},[1807,15294,3101],{},[1985,15296,2887],{},[1811,15298,2899],{},[1985,15300,1987],{},[1811,15302,15303],{},"⋅",[2881,15305,15306,15308],{},[1807,15307,3101],{},[1985,15309,9236],{},[1811,15311,1813],{},[1985,15313,1987],{},[1823,15315,15316],{"encoding":1825},"\\alpha_1=2\\alpha_2+\\alpha_3\\ \\Longrightarrow\\ \\alpha_1-2\\alpha_2-\\alpha_3+0\\cdot\\alpha_4=0",[1788,15318,15320,15376,15435,15497,15553,15611,15666,15684,15739],{"className":15319,"ariaHidden":1831},[1830],[1788,15321,15323,15327,15367,15370,15373],{"className":15322},[1835],[1788,15324],{"className":15325,"style":15326},[1839],"height:0.5806em;vertical-align:-0.15em;",[1788,15328,15330,15333],{"className":15329},[1844],[1788,15331,3101],{"className":15332,"style":3118},[1844,1845],[1788,15334,15336],{"className":15335},[1875],[1788,15337,15339,15359],{"className":15338},[1879,2931],[1788,15340,15342,15356],{"className":15341},[1883],[1788,15343,15345],{"className":15344,"style":2938},[1887],[1788,15346,15347,15350],{"style":9312},[1788,15348],{"className":15349,"style":1895},[1894],[1788,15351,15353],{"className":15352},[1899,1900,1901,1902],[1788,15354,2906],{"className":15355},[1844,1902],[1788,15357,2958],{"className":15358},[2957],[1788,15360,15362],{"className":15361},[1883],[1788,15363,15365],{"className":15364,"style":2965},[1887],[1788,15366],{},[1788,15368],{"className":15369,"style":1851},[1850],[1788,15371,1813],{"className":15372},[1855],[1788,15374],{"className":15375,"style":1851},[1850],[1788,15377,15379,15383,15386,15426,15429,15432],{"className":15378},[1835],[1788,15380],{"className":15381,"style":15382},[1839],"height:0.7944em;vertical-align:-0.15em;",[1788,15384,2896],{"className":15385},[1844],[1788,15387,15389,15392],{"className":15388},[1844],[1788,15390,3101],{"className":15391,"style":3118},[1844,1845],[1788,15393,15395],{"className":15394},[1875],[1788,15396,15398,15418],{"className":15397},[1879,2931],[1788,15399,15401,15415],{"className":15400},[1883],[1788,15402,15404],{"className":15403,"style":2938},[1887],[1788,15405,15406,15409],{"style":9312},[1788,15407],{"className":15408,"style":1895},[1894],[1788,15410,15412],{"className":15411},[1899,1900,1901,1902],[1788,15413,2896],{"className":15414},[1844,1902],[1788,15416,2958],{"className":15417},[2957],[1788,15419,15421],{"className":15420},[1883],[1788,15422,15424],{"className":15423,"style":2965},[1887],[1788,15425],{},[1788,15427],{"className":15428,"style":3029},[1850],[1788,15430,2899],{"className":15431},[3033],[1788,15433],{"className":15434,"style":3029},[1850],[1788,15436,15438,15442,15482,15485,15488,15491,15494],{"className":15437},[1835],[1788,15439],{"className":15440,"style":15441},[1839],"height:0.675em;vertical-align:-0.15em;",[1788,15443,15445,15448],{"className":15444},[1844],[1788,15446,3101],{"className":15447,"style":3118},[1844,1845],[1788,15449,15451],{"className":15450},[1875],[1788,15452,15454,15474],{"className":15453},[1879,2931],[1788,15455,15457,15471],{"className":15456},[1883],[1788,15458,15460],{"className":15459,"style":2938},[1887],[1788,15461,15462,15465],{"style":9312},[1788,15463],{"className":15464,"style":1895},[1894],[1788,15466,15468],{"className":15467},[1899,1900,1901,1902],[1788,15469,2887],{"className":15470},[1844,1902],[1788,15472,2958],{"className":15473},[2957],[1788,15475,15477],{"className":15476},[1883],[1788,15478,15480],{"className":15479,"style":2965},[1887],[1788,15481],{},[1788,15483,1973],{"className":15484},[1850],[1788,15486],{"className":15487,"style":1851},[1850],[1788,15489,15270],{"className":15490},[1855],[1788,15492,1973],{"className":15493},[1850],[1788,15495],{"className":15496,"style":1851},[1850],[1788,15498,15500,15504,15544,15547,15550],{"className":15499},[1835],[1788,15501],{"className":15502,"style":15503},[1839],"height:0.7333em;vertical-align:-0.15em;",[1788,15505,15507,15510],{"className":15506},[1844],[1788,15508,3101],{"className":15509,"style":3118},[1844,1845],[1788,15511,15513],{"className":15512},[1875],[1788,15514,15516,15536],{"className":15515},[1879,2931],[1788,15517,15519,15533],{"className":15518},[1883],[1788,15520,15522],{"className":15521,"style":2938},[1887],[1788,15523,15524,15527],{"style":9312},[1788,15525],{"className":15526,"style":1895},[1894],[1788,15528,15530],{"className":15529},[1899,1900,1901,1902],[1788,15531,2906],{"className":15532},[1844,1902],[1788,15534,2958],{"className":15535},[2957],[1788,15537,15539],{"className":15538},[1883],[1788,15540,15542],{"className":15541,"style":2965},[1887],[1788,15543],{},[1788,15545],{"className":15546,"style":3029},[1850],[1788,15548,3250],{"className":15549},[3033],[1788,15551],{"className":15552,"style":3029},[1850],[1788,15554,15556,15559,15562,15602,15605,15608],{"className":15555},[1835],[1788,15557],{"className":15558,"style":15382},[1839],[1788,15560,2896],{"className":15561},[1844],[1788,15563,15565,15568],{"className":15564},[1844],[1788,15566,3101],{"className":15567,"style":3118},[1844,1845],[1788,15569,15571],{"className":15570},[1875],[1788,15572,15574,15594],{"className":15573},[1879,2931],[1788,15575,15577,15591],{"className":15576},[1883],[1788,15578,15580],{"className":15579,"style":2938},[1887],[1788,15581,15582,15585],{"style":9312},[1788,15583],{"className":15584,"style":1895},[1894],[1788,15586,15588],{"className":15587},[1899,1900,1901,1902],[1788,15589,2896],{"className":15590},[1844,1902],[1788,15592,2958],{"className":15593},[2957],[1788,15595,15597],{"className":15596},[1883],[1788,15598,15600],{"className":15599,"style":2965},[1887],[1788,15601],{},[1788,15603],{"className":15604,"style":3029},[1850],[1788,15606,3250],{"className":15607},[3033],[1788,15609],{"className":15610,"style":3029},[1850],[1788,15612,15614,15617,15657,15660,15663],{"className":15613},[1835],[1788,15615],{"className":15616,"style":15503},[1839],[1788,15618,15620,15623],{"className":15619},[1844],[1788,15621,3101],{"className":15622,"style":3118},[1844,1845],[1788,15624,15626],{"className":15625},[1875],[1788,15627,15629,15649],{"className":15628},[1879,2931],[1788,15630,15632,15646],{"className":15631},[1883],[1788,15633,15635],{"className":15634,"style":2938},[1887],[1788,15636,15637,15640],{"style":9312},[1788,15638],{"className":15639,"style":1895},[1894],[1788,15641,15643],{"className":15642},[1899,1900,1901,1902],[1788,15644,2887],{"className":15645},[1844,1902],[1788,15647,2958],{"className":15648},[2957],[1788,15650,15652],{"className":15651},[1883],[1788,15653,15655],{"className":15654,"style":2965},[1887],[1788,15656],{},[1788,15658],{"className":15659,"style":3029},[1850],[1788,15661,2899],{"className":15662},[3033],[1788,15664],{"className":15665,"style":3029},[1850],[1788,15667,15669,15672,15675,15678,15681],{"className":15668},[1835],[1788,15670],{"className":15671,"style":4209},[1839],[1788,15673,1987],{"className":15674},[1844],[1788,15676],{"className":15677,"style":3029},[1850],[1788,15679,15303],{"className":15680},[3033],[1788,15682],{"className":15683,"style":3029},[1850],[1788,15685,15687,15690,15730,15733,15736],{"className":15686},[1835],[1788,15688],{"className":15689,"style":15326},[1839],[1788,15691,15693,15696],{"className":15692},[1844],[1788,15694,3101],{"className":15695,"style":3118},[1844,1845],[1788,15697,15699],{"className":15698},[1875],[1788,15700,15702,15722],{"className":15701},[1879,2931],[1788,15703,15705,15719],{"className":15704},[1883],[1788,15706,15708],{"className":15707,"style":2938},[1887],[1788,15709,15710,15713],{"style":9312},[1788,15711],{"className":15712,"style":1895},[1894],[1788,15714,15716],{"className":15715},[1899,1900,1901,1902],[1788,15717,9236],{"className":15718},[1844,1902],[1788,15720,2958],{"className":15721},[2957],[1788,15723,15725],{"className":15724},[1883],[1788,15726,15728],{"className":15727,"style":2965},[1887],[1788,15729],{},[1788,15731],{"className":15732,"style":1851},[1850],[1788,15734,1813],{"className":15735},[1855],[1788,15737],{"className":15738,"style":1851},[1850],[1788,15740,15742,15745],{"className":15741},[1835],[1788,15743],{"className":15744,"style":4209},[1839],[1788,15746,1987],{"className":15747},[1844],[1096,15749,15750],{},[2114,15751],{"alt":15752,"src":15753},"齐次方程组示例","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1dbfe23.png",[1096,15755,15756,15757,15845],{},"则 ",[1788,15758,15760,15794],{"className":15759},[1791],[1788,15761,15763],{"className":15762},[1795],[1797,15764,15765],{"xmlns":1799},[1801,15766,15767,15791],{},[1804,15768,15769,15771,15773,15775,15777,15779,15781,15783,15785,15787,15789],{},[1811,15770,1977],{"stretchy":1976},[1985,15772,2906],{},[1811,15774,2430],{"separator":1831},[1811,15776,3250],{},[1985,15778,2896],{},[1811,15780,2430],{"separator":1831},[1811,15782,3250],{},[1985,15784,2906],{},[1811,15786,2430],{"separator":1831},[1985,15788,1987],{},[1811,15790,1990],{"stretchy":1976},[1823,15792,15793],{"encoding":1825},"(1,-2,-1,0)",[1788,15795,15797],{"className":15796,"ariaHidden":1831},[1830],[1788,15798,15800,15803,15806,15809,15812,15815,15818,15821,15824,15827,15830,15833,15836,15839,15842],{"className":15799},[1835],[1788,15801],{"className":15802,"style":2003},[1839],[1788,15804,1977],{"className":15805},[2013],[1788,15807,2906],{"className":15808},[1844],[1788,15810,2430],{"className":15811},[2474],[1788,15813],{"className":15814,"style":2478},[1850],[1788,15816,3250],{"className":15817},[1844],[1788,15819,2896],{"className":15820},[1844],[1788,15822,2430],{"className":15823},[2474],[1788,15825],{"className":15826,"style":2478},[1850],[1788,15828,3250],{"className":15829},[1844],[1788,15831,2906],{"className":15832},[1844],[1788,15834,2430],{"className":15835},[2474],[1788,15837],{"className":15838,"style":2478},[1850],[1788,15840,1987],{"className":15841},[1844],[1788,15843,1990],{"className":15844},[2079]," 就是齐次方程组的基础解系。",[1912,15847,15848,15853],{},[1096,15849,15850],{},[1099,15851,15852],{},"非齐次线性方程组有解的条件：",[1096,15854,15855,15856,15987,15988,16108,16109,16251],{},"① 若 ",[1788,15857,15859,15897],{"className":15858},[1791],[1788,15860,15862],{"className":15861},[1795],[1797,15863,15864],{"xmlns":1799},[1801,15865,15866,15894],{},[1804,15867,15868,15870,15872,15874,15876,15878,15880,15882,15884,15886,15888,15890,15892],{},[1807,15869,2421],{},[1811,15871,1977],{"stretchy":1976},[1807,15873,2290],{},[1811,15875,1990],{"stretchy":1976},[1811,15877,1983],{"mathvariant":1982},[1807,15879,2421],{},[1811,15881,1977],{"stretchy":1976},[1811,15883,14861],{"stretchy":1976},[1807,15885,2290],{},[1811,15887,2430],{"separator":1831},[1807,15889,2444],{},[1811,15891,14871],{"stretchy":1976},[1811,15893,1990],{"stretchy":1976},[1823,15895,15896],{"encoding":1825},"r(A)\\neq r([A,b])",[1788,15898,15900,15960],{"className":15899,"ariaHidden":1831},[1830],[1788,15901,15903,15906,15909,15912,15915,15918,15921,15957],{"className":15902},[1835],[1788,15904],{"className":15905,"style":2003},[1839],[1788,15907,2421],{"className":15908,"style":1846},[1844,1845],[1788,15910,1977],{"className":15911},[2013],[1788,15913,2290],{"className":15914},[1844,1845],[1788,15916,1990],{"className":15917},[2079],[1788,15919],{"className":15920,"style":1851},[1850],[1788,15922,15924,15951,15954],{"className":15923},[1855],[1788,15925,15927],{"className":15926},[1855],[1788,15928,15930],{"className":15929},[1844,2029],[1788,15931,15933],{"className":15932},[2033],[1788,15934,15936,15939,15948],{"className":15935},[2037],[1788,15937],{"className":15938,"style":2041},[1839],[1788,15940,15942],{"className":15941},[2045],[1788,15943,15945],{"className":15944},[1844],[1788,15946,2052],{"className":15947},[1855],[1788,15949],{"className":15950},[2056],[1788,15952],{"className":15953},[1850,2060],[1788,15955,1813],{"className":15956},[1855],[1788,15958],{"className":15959,"style":1851},[1850],[1788,15961,15963,15966,15969,15972,15975,15978,15981,15984],{"className":15962},[1835],[1788,15964],{"className":15965,"style":2003},[1839],[1788,15967,2421],{"className":15968,"style":1846},[1844,1845],[1788,15970,14946],{"className":15971},[2013],[1788,15973,2290],{"className":15974},[1844,1845],[1788,15976,2430],{"className":15977},[2474],[1788,15979],{"className":15980,"style":2478},[1850],[1788,15982,2444],{"className":15983},[1844,1845],[1788,15985,14962],{"className":15986},[2079],"，则方程组无解；\n② 若 ",[1788,15989,15991,16033],{"className":15990},[1791],[1788,15992,15994],{"className":15993},[1795],[1797,15995,15996],{"xmlns":1799},[1801,15997,15998,16030],{},[1804,15999,16000,16002,16004,16006,16008,16010,16012,16014,16016,16018,16020,16022,16024,16026,16028],{},[1807,16001,2421],{},[1811,16003,1977],{"stretchy":1976},[1807,16005,2290],{},[1811,16007,1990],{"stretchy":1976},[1811,16009,1813],{},[1807,16011,2421],{},[1811,16013,1977],{"stretchy":1976},[1811,16015,14861],{"stretchy":1976},[1807,16017,2290],{},[1811,16019,2430],{"separator":1831},[1807,16021,2444],{},[1811,16023,14871],{"stretchy":1976},[1811,16025,1990],{"stretchy":1976},[1811,16027,1813],{},[1807,16029,2301],{},[1823,16031,16032],{"encoding":1825},"r(A)=r([A,b])=n",[1788,16034,16036,16063,16099],{"className":16035,"ariaHidden":1831},[1830],[1788,16037,16039,16042,16045,16048,16051,16054,16057,16060],{"className":16038},[1835],[1788,16040],{"className":16041,"style":2003},[1839],[1788,16043,2421],{"className":16044,"style":1846},[1844,1845],[1788,16046,1977],{"className":16047},[2013],[1788,16049,2290],{"className":16050},[1844,1845],[1788,16052,1990],{"className":16053},[2079],[1788,16055],{"className":16056,"style":1851},[1850],[1788,16058,1813],{"className":16059},[1855],[1788,16061],{"className":16062,"style":1851},[1850],[1788,16064,16066,16069,16072,16075,16078,16081,16084,16087,16090,16093,16096],{"className":16065},[1835],[1788,16067],{"className":16068,"style":2003},[1839],[1788,16070,2421],{"className":16071,"style":1846},[1844,1845],[1788,16073,14946],{"className":16074},[2013],[1788,16076,2290],{"className":16077},[1844,1845],[1788,16079,2430],{"className":16080},[2474],[1788,16082],{"className":16083,"style":2478},[1850],[1788,16085,2444],{"className":16086},[1844,1845],[1788,16088,14962],{"className":16089},[2079],[1788,16091],{"className":16092,"style":1851},[1850],[1788,16094,1813],{"className":16095},[1855],[1788,16097],{"className":16098,"style":1851},[1850],[1788,16100,16102,16105],{"className":16101},[1835],[1788,16103],{"className":16104,"style":3114},[1839],[1788,16106,2301],{"className":16107},[1844,1845],"，则方程组有唯一解；\n③ 若 ",[1788,16110,16112,16158],{"className":16111},[1791],[1788,16113,16115],{"className":16114},[1795],[1797,16116,16117],{"xmlns":1799},[1801,16118,16119,16155],{},[1804,16120,16121,16123,16125,16127,16129,16131,16133,16135,16137,16139,16141,16143,16145,16147,16149,16151,16153],{},[1807,16122,2421],{},[1811,16124,1977],{"stretchy":1976},[1807,16126,2290],{},[1811,16128,1990],{"stretchy":1976},[1811,16130,1813],{},[1807,16132,2421],{},[1811,16134,1977],{"stretchy":1976},[1811,16136,14861],{"stretchy":1976},[1807,16138,2290],{},[1811,16140,2430],{"separator":1831},[1807,16142,2444],{},[1811,16144,14871],{"stretchy":1976},[1811,16146,1990],{"stretchy":1976},[1811,16148,1813],{},[1807,16150,2421],{},[1811,16152,15107],{},[1807,16154,2301],{},[1823,16156,16157],{"encoding":1825},"r(A)=r([A,b])=r\u003Cn",[1788,16159,16161,16188,16224,16242],{"className":16160,"ariaHidden":1831},[1830],[1788,16162,16164,16167,16170,16173,16176,16179,16182,16185],{"className":16163},[1835],[1788,16165],{"className":16166,"style":2003},[1839],[1788,16168,2421],{"className":16169,"style":1846},[1844,1845],[1788,16171,1977],{"className":16172},[2013],[1788,16174,2290],{"className":16175},[1844,1845],[1788,16177,1990],{"className":16178},[2079],[1788,16180],{"className":16181,"style":1851},[1850],[1788,16183,1813],{"className":16184},[1855],[1788,16186],{"className":16187,"style":1851},[1850],[1788,16189,16191,16194,16197,16200,16203,16206,16209,16212,16215,16218,16221],{"className":16190},[1835],[1788,16192],{"className":16193,"style":2003},[1839],[1788,16195,2421],{"className":16196,"style":1846},[1844,1845],[1788,16198,14946],{"className":16199},[2013],[1788,16201,2290],{"className":16202},[1844,1845],[1788,16204,2430],{"className":16205},[2474],[1788,16207],{"className":16208,"style":2478},[1850],[1788,16210,2444],{"className":16211},[1844,1845],[1788,16213,14962],{"className":16214},[2079],[1788,16216],{"className":16217,"style":1851},[1850],[1788,16219,1813],{"className":16220},[1855],[1788,16222],{"className":16223,"style":1851},[1850],[1788,16225,16227,16230,16233,16236,16239],{"className":16226},[1835],[1788,16228],{"className":16229,"style":15149},[1839],[1788,16231,2421],{"className":16232,"style":1846},[1844,1845],[1788,16234],{"className":16235,"style":1851},[1850],[1788,16237,15107],{"className":16238},[1855],[1788,16240],{"className":16241,"style":1851},[1850],[1788,16243,16245,16248],{"className":16244},[1835],[1788,16246],{"className":16247,"style":3114},[1839],[1788,16249,2301],{"className":16250},[1844,1845],"，则方程组有无穷多解。",[1912,16253,16254,16259],{},[1096,16255,16256],{},[1099,16257,16258],{},"非齐次方程组的通解的求法：",[1096,16260,16261,16262,16317,16318,16373],{},"① 求 ",[1788,16263,16265,16284],{"className":16264},[1791],[1788,16266,16268],{"className":16267},[1795],[1797,16269,16270],{"xmlns":1799},[1801,16271,16272,16282],{},[1804,16273,16274,16276,16278,16280],{},[1807,16275,2290],{},[1807,16277,8230],{},[1811,16279,1813],{},[1985,16281,1987],{},[1823,16283,12804],{"encoding":1825},[1788,16285,16287,16308],{"className":16286,"ariaHidden":1831},[1830],[1788,16288,16290,16293,16296,16299,16302,16305],{"className":16289},[1835],[1788,16291],{"className":16292,"style":1840},[1839],[1788,16294,2290],{"className":16295},[1844,1845],[1788,16297,8230],{"className":16298},[1844,1845],[1788,16300],{"className":16301,"style":1851},[1850],[1788,16303,1813],{"className":16304},[1855],[1788,16306],{"className":16307,"style":1851},[1850],[1788,16309,16311,16314],{"className":16310},[1835],[1788,16312],{"className":16313,"style":4209},[1839],[1788,16315,1987],{"className":16316},[1844]," 的解；\n② 求 ",[1788,16319,16321,16340],{"className":16320},[1791],[1788,16322,16324],{"className":16323},[1795],[1797,16325,16326],{"xmlns":1799},[1801,16327,16328,16338],{},[1804,16329,16330,16332,16334,16336],{},[1807,16331,2290],{},[1807,16333,8230],{},[1811,16335,1813],{},[1807,16337,2444],{},[1823,16339,8237],{"encoding":1825},[1788,16341,16343,16364],{"className":16342,"ariaHidden":1831},[1830],[1788,16344,16346,16349,16352,16355,16358,16361],{"className":16345},[1835],[1788,16347],{"className":16348,"style":1840},[1839],[1788,16350,2290],{"className":16351},[1844,1845],[1788,16353,8230],{"className":16354},[1844,1845],[1788,16356],{"className":16357,"style":1851},[1850],[1788,16359,1813],{"className":16360},[1855],[1788,16362],{"className":16363,"style":1851},[1850],[1788,16365,16367,16370],{"className":16366},[1835],[1788,16368],{"className":16369,"style":1950},[1839],[1788,16371,2444],{"className":16372},[1844,1845]," 的一个特解；\n③ 非齐次方程组的通解＝齐次方程组的通解＋一个非齐次的特解。",[1096,16375,16376],{},[2114,16377],{"alt":16378,"src":16379},"非齐次方程组通解","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1ed632d.png",[1912,16381,16382,16506,16635],{},[1096,16383,16384,16385,16413,16414,16505],{},"如果 ",[1788,16386,16388,16401],{"className":16387},[1791],[1788,16389,16391],{"className":16390},[1795],[1797,16392,16393],{"xmlns":1799},[1801,16394,16395,16399],{},[1804,16396,16397],{},[1807,16398,2290],{},[1823,16400,2290],{"encoding":1825},[1788,16402,16404],{"className":16403,"ariaHidden":1831},[1830],[1788,16405,16407,16410],{"className":16406},[1835],[1788,16408],{"className":16409,"style":1840},[1839],[1788,16411,2290],{"className":16412},[1844,1845]," 行满秩，则 ",[1788,16415,16417,16451],{"className":16416},[1791],[1788,16418,16420],{"className":16419},[1795],[1797,16421,16422],{"xmlns":1799},[1801,16423,16424,16448],{},[1804,16425,16426,16428,16430,16432,16434,16436,16438,16440,16442,16444,16446],{},[1807,16427,2421],{},[1811,16429,1977],{"stretchy":1976},[1807,16431,2290],{},[1811,16433,1990],{"stretchy":1976},[1811,16435,1813],{},[1807,16437,2421],{},[1811,16439,1977],{"stretchy":1976},[1807,16441,2290],{},[1807,16443,2285],{"mathvariant":1982},[1807,16445,2444],{},[1811,16447,1990],{"stretchy":1976},[1823,16449,16450],{"encoding":1825},"r(A)=r(A|b)",[1788,16452,16454,16481],{"className":16453,"ariaHidden":1831},[1830],[1788,16455,16457,16460,16463,16466,16469,16472,16475,16478],{"className":16456},[1835],[1788,16458],{"className":16459,"style":2003},[1839],[1788,16461,2421],{"className":16462,"style":1846},[1844,1845],[1788,16464,1977],{"className":16465},[2013],[1788,16467,2290],{"className":16468},[1844,1845],[1788,16470,1990],{"className":16471},[2079],[1788,16473],{"className":16474,"style":1851},[1850],[1788,16476,1813],{"className":16477},[1855],[1788,16479],{"className":16480,"style":1851},[1850],[1788,16482,16484,16487,16490,16493,16496,16499,16502],{"className":16483},[1835],[1788,16485],{"className":16486,"style":2003},[1839],[1788,16488,2421],{"className":16489,"style":1846},[1844,1845],[1788,16491,1977],{"className":16492},[2013],[1788,16494,2290],{"className":16495},[1844,1845],[1788,16497,2285],{"className":16498},[1844],[1788,16500,2444],{"className":16501},[1844,1845],[1788,16503,1990],{"className":16504},[2079],"，那么方程组一定有解。",[1096,16507,16384,16508,16536,16537,8852,16580,16634],{},[1788,16509,16511,16524],{"className":16510},[1791],[1788,16512,16514],{"className":16513},[1795],[1797,16515,16516],{"xmlns":1799},[1801,16517,16518,16522],{},[1804,16519,16520],{},[1807,16521,2290],{},[1823,16523,2290],{"encoding":1825},[1788,16525,16527],{"className":16526,"ariaHidden":1831},[1830],[1788,16528,16530,16533],{"className":16529},[1835],[1788,16531],{"className":16532,"style":1840},[1839],[1788,16534,2290],{"className":16535},[1844,1845]," 列满秩，则 ",[1788,16538,16540,16559],{"className":16539},[1791],[1788,16541,16543],{"className":16542},[1795],[1797,16544,16545],{"xmlns":1799},[1801,16546,16547,16557],{},[1804,16548,16549,16551,16553,16555],{},[1807,16550,2421],{},[1811,16552,1977],{"stretchy":1976},[1807,16554,2290],{},[1811,16556,1990],{"stretchy":1976},[1823,16558,2593],{"encoding":1825},[1788,16560,16562],{"className":16561,"ariaHidden":1831},[1830],[1788,16563,16565,16568,16571,16574,16577],{"className":16564},[1835],[1788,16566],{"className":16567,"style":2003},[1839],[1788,16569,2421],{"className":16570,"style":1846},[1844,1845],[1788,16572,1977],{"className":16573},[2013],[1788,16575,2290],{"className":16576},[1844,1845],[1788,16578,1990],{"className":16579},[2079],[1788,16581,16583,16607],{"className":16582},[1791],[1788,16584,16586],{"className":16585},[1795],[1797,16587,16588],{"xmlns":1799},[1801,16589,16590,16604],{},[1804,16591,16592,16594,16596,16598,16600,16602],{},[1807,16593,2421],{},[1811,16595,1977],{"stretchy":1976},[1807,16597,2290],{},[1807,16599,2285],{"mathvariant":1982},[1807,16601,2444],{},[1811,16603,1990],{"stretchy":1976},[1823,16605,16606],{"encoding":1825},"r(A|b)",[1788,16608,16610],{"className":16609,"ariaHidden":1831},[1830],[1788,16611,16613,16616,16619,16622,16625,16628,16631],{"className":16612},[1835],[1788,16614],{"className":16615,"style":2003},[1839],[1788,16617,2421],{"className":16618,"style":1846},[1844,1845],[1788,16620,1977],{"className":16621},[2013],[1788,16623,2290],{"className":16624},[1844,1845],[1788,16626,2285],{"className":16627},[1844],[1788,16629,2444],{"className":16630},[1844,1845],[1788,16632,1990],{"className":16633},[2079]," 的关系不确定：",[1096,16636,6300,16637,16728,16729,16842,16843,16956],{},[1788,16638,16640,16674],{"className":16639},[1791],[1788,16641,16643],{"className":16642},[1795],[1797,16644,16645],{"xmlns":1799},[1801,16646,16647,16671],{},[1804,16648,16649,16651,16653,16655,16657,16659,16661,16663,16665,16667,16669],{},[1807,16650,2421],{},[1811,16652,1977],{"stretchy":1976},[1807,16654,2290],{},[1811,16656,1990],{"stretchy":1976},[1811,16658,15107],{},[1807,16660,2421],{},[1811,16662,1977],{"stretchy":1976},[1807,16664,2290],{},[1807,16666,2285],{"mathvariant":1982},[1807,16668,2444],{},[1811,16670,1990],{"stretchy":1976},[1823,16672,16673],{"encoding":1825},"r(A)\u003Cr(A|b)",[1788,16675,16677,16704],{"className":16676,"ariaHidden":1831},[1830],[1788,16678,16680,16683,16686,16689,16692,16695,16698,16701],{"className":16679},[1835],[1788,16681],{"className":16682,"style":2003},[1839],[1788,16684,2421],{"className":16685,"style":1846},[1844,1845],[1788,16687,1977],{"className":16688},[2013],[1788,16690,2290],{"className":16691},[1844,1845],[1788,16693,1990],{"className":16694},[2079],[1788,16696],{"className":16697,"style":1851},[1850],[1788,16699,15107],{"className":16700},[1855],[1788,16702],{"className":16703,"style":1851},[1850],[1788,16705,16707,16710,16713,16716,16719,16722,16725],{"className":16706},[1835],[1788,16708],{"className":16709,"style":2003},[1839],[1788,16711,2421],{"className":16712,"style":1846},[1844,1845],[1788,16714,1977],{"className":16715},[2013],[1788,16717,2290],{"className":16718},[1844,1845],[1788,16720,2285],{"className":16721},[1844],[1788,16723,2444],{"className":16724},[1844,1845],[1788,16726,1990],{"className":16727},[2079],"，则无解；\n② ",[1788,16730,16732,16770],{"className":16731},[1791],[1788,16733,16735],{"className":16734},[1795],[1797,16736,16737],{"xmlns":1799},[1801,16738,16739,16767],{},[1804,16740,16741,16743,16745,16747,16749,16751,16753,16755,16757,16759,16761,16763,16765],{},[1807,16742,2421],{},[1811,16744,1977],{"stretchy":1976},[1807,16746,2290],{},[1811,16748,1990],{"stretchy":1976},[1811,16750,1813],{},[1807,16752,2421],{},[1811,16754,1977],{"stretchy":1976},[1807,16756,2290],{},[1807,16758,2285],{"mathvariant":1982},[1807,16760,2444],{},[1811,16762,1990],{"stretchy":1976},[1811,16764,15107],{},[1807,16766,2301],{},[1823,16768,16769],{"encoding":1825},"r(A)=r(A|b)\u003Cn",[1788,16771,16773,16800,16833],{"className":16772,"ariaHidden":1831},[1830],[1788,16774,16776,16779,16782,16785,16788,16791,16794,16797],{"className":16775},[1835],[1788,16777],{"className":16778,"style":2003},[1839],[1788,16780,2421],{"className":16781,"style":1846},[1844,1845],[1788,16783,1977],{"className":16784},[2013],[1788,16786,2290],{"className":16787},[1844,1845],[1788,16789,1990],{"className":16790},[2079],[1788,16792],{"className":16793,"style":1851},[1850],[1788,16795,1813],{"className":16796},[1855],[1788,16798],{"className":16799,"style":1851},[1850],[1788,16801,16803,16806,16809,16812,16815,16818,16821,16824,16827,16830],{"className":16802},[1835],[1788,16804],{"className":16805,"style":2003},[1839],[1788,16807,2421],{"className":16808,"style":1846},[1844,1845],[1788,16810,1977],{"className":16811},[2013],[1788,16813,2290],{"className":16814},[1844,1845],[1788,16816,2285],{"className":16817},[1844],[1788,16819,2444],{"className":16820},[1844,1845],[1788,16822,1990],{"className":16823},[2079],[1788,16825],{"className":16826,"style":1851},[1850],[1788,16828,15107],{"className":16829},[1855],[1788,16831],{"className":16832,"style":1851},[1850],[1788,16834,16836,16839],{"className":16835},[1835],[1788,16837],{"className":16838,"style":3114},[1839],[1788,16840,2301],{"className":16841},[1844,1845],"，有无穷多解；\n③ ",[1788,16844,16846,16884],{"className":16845},[1791],[1788,16847,16849],{"className":16848},[1795],[1797,16850,16851],{"xmlns":1799},[1801,16852,16853,16881],{},[1804,16854,16855,16857,16859,16861,16863,16865,16867,16869,16871,16873,16875,16877,16879],{},[1807,16856,2421],{},[1811,16858,1977],{"stretchy":1976},[1807,16860,2290],{},[1811,16862,1990],{"stretchy":1976},[1811,16864,1813],{},[1807,16866,2421],{},[1811,16868,1977],{"stretchy":1976},[1807,16870,2290],{},[1807,16872,2285],{"mathvariant":1982},[1807,16874,2444],{},[1811,16876,1990],{"stretchy":1976},[1811,16878,1813],{},[1807,16880,2301],{},[1823,16882,16883],{"encoding":1825},"r(A)=r(A|b)=n",[1788,16885,16887,16914,16947],{"className":16886,"ariaHidden":1831},[1830],[1788,16888,16890,16893,16896,16899,16902,16905,16908,16911],{"className":16889},[1835],[1788,16891],{"className":16892,"style":2003},[1839],[1788,16894,2421],{"className":16895,"style":1846},[1844,1845],[1788,16897,1977],{"className":16898},[2013],[1788,16900,2290],{"className":16901},[1844,1845],[1788,16903,1990],{"className":16904},[2079],[1788,16906],{"className":16907,"style":1851},[1850],[1788,16909,1813],{"className":16910},[1855],[1788,16912],{"className":16913,"style":1851},[1850],[1788,16915,16917,16920,16923,16926,16929,16932,16935,16938,16941,16944],{"className":16916},[1835],[1788,16918],{"className":16919,"style":2003},[1839],[1788,16921,2421],{"className":16922,"style":1846},[1844,1845],[1788,16924,1977],{"className":16925},[2013],[1788,16927,2290],{"className":16928},[1844,1845],[1788,16930,2285],{"className":16931},[1844],[1788,16933,2444],{"className":16934},[1844,1845],[1788,16936,1990],{"className":16937},[2079],[1788,16939],{"className":16940,"style":1851},[1850],[1788,16942,1813],{"className":16943},[1855],[1788,16945],{"className":16946,"style":1851},[1850],[1788,16948,16950,16953],{"className":16949},[1835],[1788,16951],{"className":16952,"style":3114},[1839],[1788,16954,2301],{"className":16955},[1844,1845],"，有唯一解。",[1096,16958,16959],{},[1099,16960,16961],{},"非齐次方程组解的性质：",[1912,16963,16964,17292],{},[1096,16965,7227,16966,17147,17148,17203,17204,17235,17236,17291],{},[1788,16967,16969,17004],{"className":16968},[1791],[1788,16970,16972],{"className":16971},[1795],[1797,16973,16974],{"xmlns":1799},[1801,16975,16976,17001],{},[1804,16977,16978,16985,16987,16993,16995],{},[2881,16979,16980,16983],{},[1807,16981,16982],{},"η",[1985,16984,2906],{},[1811,16986,2430],{"separator":1831},[2881,16988,16989,16991],{},[1807,16990,16982],{},[1985,16992,2896],{},[1811,16994,2430],{"separator":1831},[2881,16996,16997,16999],{},[1807,16998,16982],{},[1985,17000,2887],{},[1823,17002,17003],{"encoding":1825},"\\eta_1,\\eta_2,\\eta_3",[1788,17005,17007],{"className":17006,"ariaHidden":1831},[1830],[1788,17008,17010,17013,17055,17058,17061,17101,17104,17107],{"className":17009},[1835],[1788,17011],{"className":17012,"style":5356},[1839],[1788,17014,17016,17020],{"className":17015},[1844],[1788,17017,16982],{"className":17018,"style":17019},[1844,1845],"margin-right:0.0359em;",[1788,17021,17023],{"className":17022},[1875],[1788,17024,17026,17047],{"className":17025},[1879,2931],[1788,17027,17029,17044],{"className":17028},[1883],[1788,17030,17032],{"className":17031,"style":2938},[1887],[1788,17033,17035,17038],{"style":17034},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1788,17036],{"className":17037,"style":1895},[1894],[1788,17039,17041],{"className":17040},[1899,1900,1901,1902],[1788,17042,2906],{"className":17043},[1844,1902],[1788,17045,2958],{"className":17046},[2957],[1788,17048,17050],{"className":17049},[1883],[1788,17051,17053],{"className":17052,"style":2965},[1887],[1788,17054],{},[1788,17056,2430],{"className":17057},[2474],[1788,17059],{"className":17060,"style":2478},[1850],[1788,17062,17064,17067],{"className":17063},[1844],[1788,17065,16982],{"className":17066,"style":17019},[1844,1845],[1788,17068,17070],{"className":17069},[1875],[1788,17071,17073,17093],{"className":17072},[1879,2931],[1788,17074,17076,17090],{"className":17075},[1883],[1788,17077,17079],{"className":17078,"style":2938},[1887],[1788,17080,17081,17084],{"style":17034},[1788,17082],{"className":17083,"style":1895},[1894],[1788,17085,17087],{"className":17086},[1899,1900,1901,1902],[1788,17088,2896],{"className":17089},[1844,1902],[1788,17091,2958],{"className":17092},[2957],[1788,17094,17096],{"className":17095},[1883],[1788,17097,17099],{"className":17098,"style":2965},[1887],[1788,17100],{},[1788,17102,2430],{"className":17103},[2474],[1788,17105],{"className":17106,"style":2478},[1850],[1788,17108,17110,17113],{"className":17109},[1844],[1788,17111,16982],{"className":17112,"style":17019},[1844,1845],[1788,17114,17116],{"className":17115},[1875],[1788,17117,17119,17139],{"className":17118},[1879,2931],[1788,17120,17122,17136],{"className":17121},[1883],[1788,17123,17125],{"className":17124,"style":2938},[1887],[1788,17126,17127,17130],{"style":17034},[1788,17128],{"className":17129,"style":1895},[1894],[1788,17131,17133],{"className":17132},[1899,1900,1901,1902],[1788,17134,2887],{"className":17135},[1844,1902],[1788,17137,2958],{"className":17138},[2957],[1788,17140,17142],{"className":17141},[1883],[1788,17143,17145],{"className":17144,"style":2965},[1887],[1788,17146],{}," 是非齐次线性方程组 ",[1788,17149,17151,17170],{"className":17150},[1791],[1788,17152,17154],{"className":17153},[1795],[1797,17155,17156],{"xmlns":1799},[1801,17157,17158,17168],{},[1804,17159,17160,17162,17164,17166],{},[1807,17161,2290],{},[1807,17163,8230],{},[1811,17165,1813],{},[1807,17167,2444],{},[1823,17169,8237],{"encoding":1825},[1788,17171,17173,17194],{"className":17172,"ariaHidden":1831},[1830],[1788,17174,17176,17179,17182,17185,17188,17191],{"className":17175},[1835],[1788,17177],{"className":17178,"style":1840},[1839],[1788,17180,2290],{"className":17181},[1844,1845],[1788,17183,8230],{"className":17184},[1844,1845],[1788,17186],{"className":17187,"style":1851},[1850],[1788,17189,1813],{"className":17190},[1855],[1788,17192],{"className":17193,"style":1851},[1850],[1788,17195,17197,17200],{"className":17196},[1835],[1788,17198],{"className":17199,"style":1950},[1839],[1788,17201,2444],{"className":17202},[1844,1845]," 的解，",[1788,17205,17207,17222],{"className":17206},[1791],[1788,17208,17210],{"className":17209},[1795],[1797,17211,17212],{"xmlns":1799},[1801,17213,17214,17219],{},[1804,17215,17216],{},[1807,17217,17218],{},"ξ",[1823,17220,17221],{"encoding":1825},"\\xi",[1788,17223,17225],{"className":17224,"ariaHidden":1831},[1830],[1788,17226,17228,17231],{"className":17227},[1835],[1788,17229],{"className":17230,"style":2041},[1839],[1788,17232,17218],{"className":17233,"style":17234},[1844,1845],"margin-right:0.046em;"," 是对应齐次方程组 ",[1788,17237,17239,17258],{"className":17238},[1791],[1788,17240,17242],{"className":17241},[1795],[1797,17243,17244],{"xmlns":1799},[1801,17245,17246,17256],{},[1804,17247,17248,17250,17252,17254],{},[1807,17249,2290],{},[1807,17251,8230],{},[1811,17253,1813],{},[1985,17255,1987],{},[1823,17257,12804],{"encoding":1825},[1788,17259,17261,17282],{"className":17260,"ariaHidden":1831},[1830],[1788,17262,17264,17267,17270,17273,17276,17279],{"className":17263},[1835],[1788,17265],{"className":17266,"style":1840},[1839],[1788,17268,2290],{"className":17269},[1844,1845],[1788,17271,8230],{"className":17272},[1844,1845],[1788,17274],{"className":17275,"style":1851},[1850],[1788,17277,1813],{"className":17278},[1855],[1788,17280],{"className":17281,"style":1851},[1850],[1788,17283,17285,17288],{"className":17284},[1835],[1788,17286],{"className":17287,"style":4209},[1839],[1788,17289,1987],{"className":17290},[1844]," 的解，则：",[1096,17293,17294,17295,4896,17429,17484,17485,4896,17541,17596],{},"（1）",[1788,17296,17298,17324],{"className":17297},[1791],[1788,17299,17301],{"className":17300},[1795],[1797,17302,17303],{"xmlns":1799},[1801,17304,17305,17321],{},[1804,17306,17307,17313,17315],{},[2881,17308,17309,17311],{},[1807,17310,16982],{},[1985,17312,2906],{},[1811,17314,3250],{},[2881,17316,17317,17319],{},[1807,17318,16982],{},[1985,17320,2896],{},[1823,17322,17323],{"encoding":1825},"\\eta_1-\\eta_2",[1788,17325,17327,17383],{"className":17326,"ariaHidden":1831},[1830],[1788,17328,17330,17334,17374,17377,17380],{"className":17329},[1835],[1788,17331],{"className":17332,"style":17333},[1839],"height:0.7778em;vertical-align:-0.1944em;",[1788,17335,17337,17340],{"className":17336},[1844],[1788,17338,16982],{"className":17339,"style":17019},[1844,1845],[1788,17341,17343],{"className":17342},[1875],[1788,17344,17346,17366],{"className":17345},[1879,2931],[1788,17347,17349,17363],{"className":17348},[1883],[1788,17350,17352],{"className":17351,"style":2938},[1887],[1788,17353,17354,17357],{"style":17034},[1788,17355],{"className":17356,"style":1895},[1894],[1788,17358,17360],{"className":17359},[1899,1900,1901,1902],[1788,17361,2906],{"className":17362},[1844,1902],[1788,17364,2958],{"className":17365},[2957],[1788,17367,17369],{"className":17368},[1883],[1788,17370,17372],{"className":17371,"style":2965},[1887],[1788,17373],{},[1788,17375],{"className":17376,"style":3029},[1850],[1788,17378,3250],{"className":17379},[3033],[1788,17381],{"className":17382,"style":3029},[1850],[1788,17384,17386,17389],{"className":17385},[1835],[1788,17387],{"className":17388,"style":5356},[1839],[1788,17390,17392,17395],{"className":17391},[1844],[1788,17393,16982],{"className":17394,"style":17019},[1844,1845],[1788,17396,17398],{"className":17397},[1875],[1788,17399,17401,17421],{"className":17400},[1879,2931],[1788,17402,17404,17418],{"className":17403},[1883],[1788,17405,17407],{"className":17406,"style":2938},[1887],[1788,17408,17409,17412],{"style":17034},[1788,17410],{"className":17411,"style":1895},[1894],[1788,17413,17415],{"className":17414},[1899,1900,1901,1902],[1788,17416,2896],{"className":17417},[1844,1902],[1788,17419,2958],{"className":17420},[2957],[1788,17422,17424],{"className":17423},[1883],[1788,17425,17427],{"className":17426,"style":2965},[1887],[1788,17428],{},[1788,17430,17432,17451],{"className":17431},[1791],[1788,17433,17435],{"className":17434},[1795],[1797,17436,17437],{"xmlns":1799},[1801,17438,17439,17449],{},[1804,17440,17441,17443,17445,17447],{},[1807,17442,2290],{},[1807,17444,8230],{},[1811,17446,1813],{},[1985,17448,1987],{},[1823,17450,12804],{"encoding":1825},[1788,17452,17454,17475],{"className":17453,"ariaHidden":1831},[1830],[1788,17455,17457,17460,17463,17466,17469,17472],{"className":17456},[1835],[1788,17458],{"className":17459,"style":1840},[1839],[1788,17461,2290],{"className":17462},[1844,1845],[1788,17464,8230],{"className":17465},[1844,1845],[1788,17467],{"className":17468,"style":1851},[1850],[1788,17470,1813],{"className":17471},[1855],[1788,17473],{"className":17474,"style":1851},[1850],[1788,17476,17478,17481],{"className":17477},[1835],[1788,17479],{"className":17480,"style":4209},[1839],[1788,17482,1987],{"className":17483},[1844]," 的解；\n（2）",[1788,17486,17488,17508],{"className":17487},[1791],[1788,17489,17491],{"className":17490},[1795],[1797,17492,17493],{"xmlns":1799},[1801,17494,17495,17505],{},[1804,17496,17497,17499,17501,17503],{},[1807,17498,1938],{},[1807,17500,17218],{},[1811,17502,2899],{},[1807,17504,16982],{},[1823,17506,17507],{"encoding":1825},"k\\xi+\\eta",[1788,17509,17511,17532],{"className":17510,"ariaHidden":1831},[1830],[1788,17512,17514,17517,17520,17523,17526,17529],{"className":17513},[1835],[1788,17515],{"className":17516,"style":2041},[1839],[1788,17518,1938],{"className":17519,"style":1954},[1844,1845],[1788,17521,17218],{"className":17522,"style":17234},[1844,1845],[1788,17524],{"className":17525,"style":3029},[1850],[1788,17527,2899],{"className":17528},[3033],[1788,17530],{"className":17531,"style":3029},[1850],[1788,17533,17535,17538],{"className":17534},[1835],[1788,17536],{"className":17537,"style":5356},[1839],[1788,17539,16982],{"className":17540,"style":17019},[1844,1845],[1788,17542,17544,17563],{"className":17543},[1791],[1788,17545,17547],{"className":17546},[1795],[1797,17548,17549],{"xmlns":1799},[1801,17550,17551,17561],{},[1804,17552,17553,17555,17557,17559],{},[1807,17554,2290],{},[1807,17556,8230],{},[1811,17558,1813],{},[1807,17560,2444],{},[1823,17562,8237],{"encoding":1825},[1788,17564,17566,17587],{"className":17565,"ariaHidden":1831},[1830],[1788,17567,17569,17572,17575,17578,17581,17584],{"className":17568},[1835],[1788,17570],{"className":17571,"style":1840},[1839],[1788,17573,2290],{"className":17574},[1844,1845],[1788,17576,8230],{"className":17577},[1844,1845],[1788,17579],{"className":17580,"style":1851},[1850],[1788,17582,1813],{"className":17583},[1855],[1788,17585],{"className":17586,"style":1851},[1850],[1788,17588,17590,17593],{"className":17589},[1835],[1788,17591],{"className":17592,"style":1950},[1839],[1788,17594,2444],{"className":17595},[1844,1845]," 的解。",[1096,17598,17599],{},"扩展：",[1096,17601,17602],{},[2114,17603],{"alt":17604,"src":17605},"解的性质扩展","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1ec96b0.png",[1912,17607,17608,17611],{},[1096,17609,17610],{},"解释：",[1918,17612,17613,17673,18119,18569,18572],{},[1921,17614,17615,17643,17644,17672],{},[1788,17616,17618,17631],{"className":17617},[1791],[1788,17619,17621],{"className":17620},[1795],[1797,17622,17623],{"xmlns":1799},[1801,17624,17625,17629],{},[1804,17626,17627],{},[1807,17628,1096],{},[1823,17630,1096],{"encoding":1825},[1788,17632,17634],{"className":17633,"ariaHidden":1831},[1830],[1788,17635,17637,17640],{"className":17636},[1835],[1788,17638],{"className":17639,"style":5356},[1839],[1788,17641,1096],{"className":17642},[1844,1845]," 个解的任意组合，系数之和为 ",[1788,17645,17647,17660],{"className":17646},[1791],[1788,17648,17650],{"className":17649},[1795],[1797,17651,17652],{"xmlns":1799},[1801,17653,17654,17658],{},[1804,17655,17656],{},[1985,17657,1987],{},[1823,17659,1987],{"encoding":1825},[1788,17661,17663],{"className":17662,"ariaHidden":1831},[1830],[1788,17664,17666,17669],{"className":17665},[1835],[1788,17667],{"className":17668,"style":4209},[1839],[1788,17670,1987],{"className":17671},[1844]," 时，是齐次线性方程组的解；",[1921,17674,17675,17676,17920,17921,18118],{},"非齐次的解线性组合也能得到齐次线性方程组的解，但需要满足 ",[1788,17677,17679,17721],{"className":17678},[1791],[1788,17680,17682],{"className":17681},[1795],[1797,17683,17684],{"xmlns":1799},[1801,17685,17686,17718],{},[1804,17687,17688,17694,17696,17702,17704,17706,17708,17714,17716],{},[2881,17689,17690,17692],{},[1807,17691,1938],{},[1985,17693,2906],{},[1811,17695,2899],{},[2881,17697,17698,17700],{},[1807,17699,1938],{},[1985,17701,2896],{},[1811,17703,2899],{},[1811,17705,9241],{},[1811,17707,2899],{},[2881,17709,17710,17712],{},[1807,17711,1938],{},[1807,17713,1096],{},[1811,17715,1813],{},[1985,17717,1987],{},[1823,17719,17720],{"encoding":1825},"k_1+k_2+\\cdots+k_p=0",[1788,17722,17724,17781,17836,17854,17911],{"className":17723,"ariaHidden":1831},[1830],[1788,17725,17727,17731,17772,17775,17778],{"className":17726},[1835],[1788,17728],{"className":17729,"style":17730},[1839],"height:0.8444em;vertical-align:-0.15em;",[1788,17732,17734,17737],{"className":17733},[1844],[1788,17735,1938],{"className":17736,"style":1954},[1844,1845],[1788,17738,17740],{"className":17739},[1875],[1788,17741,17743,17764],{"className":17742},[1879,2931],[1788,17744,17746,17761],{"className":17745},[1883],[1788,17747,17749],{"className":17748,"style":2938},[1887],[1788,17750,17752,17755],{"style":17751},"top:-2.55em;margin-left:-0.0315em;margin-right:0.05em;",[1788,17753],{"className":17754,"style":1895},[1894],[1788,17756,17758],{"className":17757},[1899,1900,1901,1902],[1788,17759,2906],{"className":17760},[1844,1902],[1788,17762,2958],{"className":17763},[2957],[1788,17765,17767],{"className":17766},[1883],[1788,17768,17770],{"className":17769,"style":2965},[1887],[1788,17771],{},[1788,17773],{"className":17774,"style":3029},[1850],[1788,17776,2899],{"className":17777},[3033],[1788,17779],{"className":17780,"style":3029},[1850],[1788,17782,17784,17787,17827,17830,17833],{"className":17783},[1835],[1788,17785],{"className":17786,"style":17730},[1839],[1788,17788,17790,17793],{"className":17789},[1844],[1788,17791,1938],{"className":17792,"style":1954},[1844,1845],[1788,17794,17796],{"className":17795},[1875],[1788,17797,17799,17819],{"className":17798},[1879,2931],[1788,17800,17802,17816],{"className":17801},[1883],[1788,17803,17805],{"className":17804,"style":2938},[1887],[1788,17806,17807,17810],{"style":17751},[1788,17808],{"className":17809,"style":1895},[1894],[1788,17811,17813],{"className":17812},[1899,1900,1901,1902],[1788,17814,2896],{"className":17815},[1844,1902],[1788,17817,2958],{"className":17818},[2957],[1788,17820,17822],{"className":17821},[1883],[1788,17823,17825],{"className":17824,"style":2965},[1887],[1788,17826],{},[1788,17828],{"className":17829,"style":3029},[1850],[1788,17831,2899],{"className":17832},[3033],[1788,17834],{"className":17835,"style":3029},[1850],[1788,17837,17839,17842,17845,17848,17851],{"className":17838},[1835],[1788,17840],{"className":17841,"style":4190},[1839],[1788,17843,9241],{"className":17844},[9480],[1788,17846],{"className":17847,"style":3029},[1850],[1788,17849,2899],{"className":17850},[3033],[1788,17852],{"className":17853,"style":3029},[1850],[1788,17855,17857,17861,17902,17905,17908],{"className":17856},[1835],[1788,17858],{"className":17859,"style":17860},[1839],"height:0.9805em;vertical-align:-0.2861em;",[1788,17862,17864,17867],{"className":17863},[1844],[1788,17865,1938],{"className":17866,"style":1954},[1844,1845],[1788,17868,17870],{"className":17869},[1875],[1788,17871,17873,17894],{"className":17872},[1879,2931],[1788,17874,17876,17891],{"className":17875},[1883],[1788,17877,17880],{"className":17878,"style":17879},[1887],"height:0.1514em;",[1788,17881,17882,17885],{"style":17751},[1788,17883],{"className":17884,"style":1895},[1894],[1788,17886,17888],{"className":17887},[1899,1900,1901,1902],[1788,17889,1096],{"className":17890},[1844,1845,1902],[1788,17892,2958],{"className":17893},[2957],[1788,17895,17897],{"className":17896},[1883],[1788,17898,17900],{"className":17899,"style":4096},[1887],[1788,17901],{},[1788,17903],{"className":17904,"style":1851},[1850],[1788,17906,1813],{"className":17907},[1855],[1788,17909],{"className":17910,"style":1851},[1850],[1788,17912,17914,17917],{"className":17913},[1835],[1788,17915],{"className":17916,"style":4209},[1839],[1788,17918,1987],{"className":17919},[1844],"，例如 ",[1788,17922,17924,17966],{"className":17923},[1791],[1788,17925,17927],{"className":17926},[1795],[1797,17928,17929],{"xmlns":1799},[1801,17930,17931,17963],{},[1804,17932,17933,17939,17941,17947,17949,17951,17953,17955,17957,17959,17961],{},[2881,17934,17935,17937],{},[1807,17936,3101],{},[1985,17938,2906],{},[1811,17940,3250],{},[2881,17942,17943,17945],{},[1807,17944,3101],{},[1985,17946,2896],{},[1971,17948,1973],{},[1811,17950,1977],{"stretchy":1976},[1985,17952,2906],{},[1811,17954,3250],{},[1985,17956,2906],{},[1811,17958,1813],{},[1985,17960,1987],{},[1811,17962,1990],{"stretchy":1976},[1823,17964,17965],{"encoding":1825},"\\alpha_1-\\alpha_2\\ (1-1=0)",[1788,17967,17969,18024,18088,18106],{"className":17968,"ariaHidden":1831},[1830],[1788,17970,17972,17975,18015,18018,18021],{"className":17971},[1835],[1788,17973],{"className":17974,"style":15503},[1839],[1788,17976,17978,17981],{"className":17977},[1844],[1788,17979,3101],{"className":17980,"style":3118},[1844,1845],[1788,17982,17984],{"className":17983},[1875],[1788,17985,17987,18007],{"className":17986},[1879,2931],[1788,17988,17990,18004],{"className":17989},[1883],[1788,17991,17993],{"className":17992,"style":2938},[1887],[1788,17994,17995,17998],{"style":9312},[1788,17996],{"className":17997,"style":1895},[1894],[1788,17999,18001],{"className":18000},[1899,1900,1901,1902],[1788,18002,2906],{"className":18003},[1844,1902],[1788,18005,2958],{"className":18006},[2957],[1788,18008,18010],{"className":18009},[1883],[1788,18011,18013],{"className":18012,"style":2965},[1887],[1788,18014],{},[1788,18016],{"className":18017,"style":3029},[1850],[1788,18019,3250],{"className":18020},[3033],[1788,18022],{"className":18023,"style":3029},[1850],[1788,18025,18027,18030,18070,18073,18076,18079,18082,18085],{"className":18026},[1835],[1788,18028],{"className":18029,"style":2003},[1839],[1788,18031,18033,18036],{"className":18032},[1844],[1788,18034,3101],{"className":18035,"style":3118},[1844,1845],[1788,18037,18039],{"className":18038},[1875],[1788,18040,18042,18062],{"className":18041},[1879,2931],[1788,18043,18045,18059],{"className":18044},[1883],[1788,18046,18048],{"className":18047,"style":2938},[1887],[1788,18049,18050,18053],{"style":9312},[1788,18051],{"className":18052,"style":1895},[1894],[1788,18054,18056],{"className":18055},[1899,1900,1901,1902],[1788,18057,2896],{"className":18058},[1844,1902],[1788,18060,2958],{"className":18061},[2957],[1788,18063,18065],{"className":18064},[1883],[1788,18066,18068],{"className":18067,"style":2965},[1887],[1788,18069],{},[1788,18071,1973],{"className":18072},[1850],[1788,18074,1977],{"className":18075},[2013],[1788,18077,2906],{"className":18078},[1844],[1788,18080],{"className":18081,"style":3029},[1850],[1788,18083,3250],{"className":18084},[3033],[1788,18086],{"className":18087,"style":3029},[1850],[1788,18089,18091,18094,18097,18100,18103],{"className":18090},[1835],[1788,18092],{"className":18093,"style":4209},[1839],[1788,18095,2906],{"className":18096},[1844],[1788,18098],{"className":18099,"style":1851},[1850],[1788,18101,1813],{"className":18102},[1855],[1788,18104],{"className":18105,"style":1851},[1850],[1788,18107,18109,18112,18115],{"className":18108},[1835],[1788,18110],{"className":18111,"style":2003},[1839],[1788,18113,1987],{"className":18114},[1844],[1788,18116,1990],{"className":18117},[2079]," 就是齐次线性方程组的解；",[1921,18120,18121,18122,17920,18362,18568],{},"非齐次的解线性组合也能得到非齐次线性方程组的解，但需要满足 ",[1788,18123,18125,18167],{"className":18124},[1791],[1788,18126,18128],{"className":18127},[1795],[1797,18129,18130],{"xmlns":1799},[1801,18131,18132,18164],{},[1804,18133,18134,18140,18142,18148,18150,18152,18154,18160,18162],{},[2881,18135,18136,18138],{},[1807,18137,1938],{},[1985,18139,2906],{},[1811,18141,2899],{},[2881,18143,18144,18146],{},[1807,18145,1938],{},[1985,18147,2896],{},[1811,18149,2899],{},[1811,18151,9241],{},[1811,18153,2899],{},[2881,18155,18156,18158],{},[1807,18157,1938],{},[1807,18159,1096],{},[1811,18161,1813],{},[1985,18163,2906],{},[1823,18165,18166],{"encoding":1825},"k_1+k_2+\\cdots+k_p=1",[1788,18168,18170,18225,18280,18298,18353],{"className":18169,"ariaHidden":1831},[1830],[1788,18171,18173,18176,18216,18219,18222],{"className":18172},[1835],[1788,18174],{"className":18175,"style":17730},[1839],[1788,18177,18179,18182],{"className":18178},[1844],[1788,18180,1938],{"className":18181,"style":1954},[1844,1845],[1788,18183,18185],{"className":18184},[1875],[1788,18186,18188,18208],{"className":18187},[1879,2931],[1788,18189,18191,18205],{"className":18190},[1883],[1788,18192,18194],{"className":18193,"style":2938},[1887],[1788,18195,18196,18199],{"style":17751},[1788,18197],{"className":18198,"style":1895},[1894],[1788,18200,18202],{"className":18201},[1899,1900,1901,1902],[1788,18203,2906],{"className":18204},[1844,1902],[1788,18206,2958],{"className":18207},[2957],[1788,18209,18211],{"className":18210},[1883],[1788,18212,18214],{"className":18213,"style":2965},[1887],[1788,18215],{},[1788,18217],{"className":18218,"style":3029},[1850],[1788,18220,2899],{"className":18221},[3033],[1788,18223],{"className":18224,"style":3029},[1850],[1788,18226,18228,18231,18271,18274,18277],{"className":18227},[1835],[1788,18229],{"className":18230,"style":17730},[1839],[1788,18232,18234,18237],{"className":18233},[1844],[1788,18235,1938],{"className":18236,"style":1954},[1844,1845],[1788,18238,18240],{"className":18239},[1875],[1788,18241,18243,18263],{"className":18242},[1879,2931],[1788,18244,18246,18260],{"className":18245},[1883],[1788,18247,18249],{"className":18248,"style":2938},[1887],[1788,18250,18251,18254],{"style":17751},[1788,18252],{"className":18253,"style":1895},[1894],[1788,18255,18257],{"className":18256},[1899,1900,1901,1902],[1788,18258,2896],{"className":18259},[1844,1902],[1788,18261,2958],{"className":18262},[2957],[1788,18264,18266],{"className":18265},[1883],[1788,18267,18269],{"className":18268,"style":2965},[1887],[1788,18270],{},[1788,18272],{"className":18273,"style":3029},[1850],[1788,18275,2899],{"className":18276},[3033],[1788,18278],{"className":18279,"style":3029},[1850],[1788,18281,18283,18286,18289,18292,18295],{"className":18282},[1835],[1788,18284],{"className":18285,"style":4190},[1839],[1788,18287,9241],{"className":18288},[9480],[1788,18290],{"className":18291,"style":3029},[1850],[1788,18293,2899],{"className":18294},[3033],[1788,18296],{"className":18297,"style":3029},[1850],[1788,18299,18301,18304,18344,18347,18350],{"className":18300},[1835],[1788,18302],{"className":18303,"style":17860},[1839],[1788,18305,18307,18310],{"className":18306},[1844],[1788,18308,1938],{"className":18309,"style":1954},[1844,1845],[1788,18311,18313],{"className":18312},[1875],[1788,18314,18316,18336],{"className":18315},[1879,2931],[1788,18317,18319,18333],{"className":18318},[1883],[1788,18320,18322],{"className":18321,"style":17879},[1887],[1788,18323,18324,18327],{"style":17751},[1788,18325],{"className":18326,"style":1895},[1894],[1788,18328,18330],{"className":18329},[1899,1900,1901,1902],[1788,18331,1096],{"className":18332},[1844,1845,1902],[1788,18334,2958],{"className":18335},[2957],[1788,18337,18339],{"className":18338},[1883],[1788,18340,18342],{"className":18341,"style":4096},[1887],[1788,18343],{},[1788,18345],{"className":18346,"style":1851},[1850],[1788,18348,1813],{"className":18349},[1855],[1788,18351],{"className":18352,"style":1851},[1850],[1788,18354,18356,18359],{"className":18355},[1835],[1788,18357],{"className":18358,"style":4209},[1839],[1788,18360,2906],{"className":18361},[1844],[1788,18363,18365,18401],{"className":18364},[1791],[1788,18366,18368],{"className":18367},[1795],[1797,18369,18370],{"xmlns":1799},[1801,18371,18372,18398],{},[1804,18373,18374],{},[18375,18376,18377],"mstyle",{"scriptlevel":1987,"displaystyle":1831},[18378,18379,18380,18396],"mfrac",{},[1804,18381,18382,18388,18390],{},[2881,18383,18384,18386],{},[1807,18385,3101],{},[1985,18387,2906],{},[1811,18389,2899],{},[2881,18391,18392,18394],{},[1807,18393,3101],{},[1985,18395,2896],{},[1985,18397,2896],{},[1823,18399,18400],{"encoding":1825},"\\dfrac{\\alpha_1+\\alpha_2}{2}",[1788,18402,18404],{"className":18403,"ariaHidden":1831},[1830],[1788,18405,18407,18411],{"className":18406},[1835],[1788,18408],{"className":18409,"style":18410},[1839],"height:1.9463em;vertical-align:-0.686em;",[1788,18412,18414,18418,18565],{"className":18413},[1844],[1788,18415],{"className":18416},[2013,18417],"nulldelimiter",[1788,18419,18421],{"className":18420},[18378],[1788,18422,18424,18556],{"className":18423},[1879,2931],[1788,18425,18427,18553],{"className":18426},[1883],[1788,18428,18431,18444,18455],{"className":18429,"style":18430},[1887],"height:1.2603em;",[1788,18432,18434,18438],{"style":18433},"top:-2.314em;",[1788,18435],{"className":18436,"style":18437},[1894],"height:3em;",[1788,18439,18441],{"className":18440},[1844],[1788,18442,2896],{"className":18443},[1844],[1788,18445,18447,18450],{"style":18446},"top:-3.23em;",[1788,18448],{"className":18449,"style":18437},[1894],[1788,18451],{"className":18452,"style":18454},[18453],"frac-line","border-bottom-width:0.04em;",[1788,18456,18458,18461],{"style":18457},"top:-3.677em;",[1788,18459],{"className":18460,"style":18437},[1894],[1788,18462,18464,18504,18507,18510,18513],{"className":18463},[1844],[1788,18465,18467,18470],{"className":18466},[1844],[1788,18468,3101],{"className":18469,"style":3118},[1844,1845],[1788,18471,18473],{"className":18472},[1875],[1788,18474,18476,18496],{"className":18475},[1879,2931],[1788,18477,18479,18493],{"className":18478},[1883],[1788,18480,18482],{"className":18481,"style":2938},[1887],[1788,18483,18484,18487],{"style":9312},[1788,18485],{"className":18486,"style":1895},[1894],[1788,18488,18490],{"className":18489},[1899,1900,1901,1902],[1788,18491,2906],{"className":18492},[1844,1902],[1788,18494,2958],{"className":18495},[2957],[1788,18497,18499],{"className":18498},[1883],[1788,18500,18502],{"className":18501,"style":2965},[1887],[1788,18503],{},[1788,18505],{"className":18506,"style":3029},[1850],[1788,18508,2899],{"className":18509},[3033],[1788,18511],{"className":18512,"style":3029},[1850],[1788,18514,18516,18519],{"className":18515},[1844],[1788,18517,3101],{"className":18518,"style":3118},[1844,1845],[1788,18520,18522],{"className":18521},[1875],[1788,18523,18525,18545],{"className":18524},[1879,2931],[1788,18526,18528,18542],{"className":18527},[1883],[1788,18529,18531],{"className":18530,"style":2938},[1887],[1788,18532,18533,18536],{"style":9312},[1788,18534],{"className":18535,"style":1895},[1894],[1788,18537,18539],{"className":18538},[1899,1900,1901,1902],[1788,18540,2896],{"className":18541},[1844,1902],[1788,18543,2958],{"className":18544},[2957],[1788,18546,18548],{"className":18547},[1883],[1788,18549,18551],{"className":18550,"style":2965},[1887],[1788,18552],{},[1788,18554,2958],{"className":18555},[2957],[1788,18557,18559],{"className":18558},[1883],[1788,18560,18563],{"className":18561,"style":18562},[1887],"height:0.686em;",[1788,18564],{},[1788,18566],{"className":18567},[2079,18417]," 就是非齐次线性方程组的一个解；",[1921,18570,18571],{},"齐次线性方程组的解与非齐次线性方程组的解相加，得到的是非齐次线性方程组的解；",[1921,18573,18574,3086,18640,18668,18669,18719,18720,18935,18936,18991,18992,19042,19043,4896,19430,17596],{},[1788,18575,18577,18601],{"className":18576},[1791],[1788,18578,18580],{"className":18579},[1795],[1797,18581,18582],{"xmlns":1799},[1801,18583,18584,18598],{},[1804,18585,18586,18588,18590,18592,18594,18596],{},[1807,18587,2421],{},[1811,18589,1977],{"stretchy":1976},[1807,18591,2290],{},[1811,18593,1990],{"stretchy":1976},[1811,18595,1813],{},[1807,18597,2421],{},[1823,18599,18600],{"encoding":1825},"r(A)=r",[1788,18602,18604,18631],{"className":18603,"ariaHidden":1831},[1830],[1788,18605,18607,18610,18613,18616,18619,18622,18625,18628],{"className":18606},[1835],[1788,18608],{"className":18609,"style":2003},[1839],[1788,18611,2421],{"className":18612,"style":1846},[1844,1845],[1788,18614,1977],{"className":18615},[2013],[1788,18617,2290],{"className":18618},[1844,1845],[1788,18620,1990],{"className":18621},[2079],[1788,18623],{"className":18624,"style":1851},[1850],[1788,18626,1813],{"className":18627},[1855],[1788,18629],{"className":18630,"style":1851},[1850],[1788,18632,18634,18637],{"className":18633},[1835],[1788,18635],{"className":18636,"style":3114},[1839],[1788,18638,2421],{"className":18639,"style":1846},[1844,1845],[1788,18641,18643,18656],{"className":18642},[1791],[1788,18644,18646],{"className":18645},[1795],[1797,18647,18648],{"xmlns":1799},[1801,18649,18650,18654],{},[1804,18651,18652],{},[1807,18653,2290],{},[1823,18655,2290],{"encoding":1825},[1788,18657,18659],{"className":18658,"ariaHidden":1831},[1830],[1788,18660,18662,18665],{"className":18661},[1835],[1788,18663],{"className":18664,"style":1840},[1839],[1788,18666,2290],{"className":18667},[1844,1845]," 就有 ",[1788,18670,18672,18689],{"className":18671},[1791],[1788,18673,18675],{"className":18674},[1795],[1797,18676,18677],{"xmlns":1799},[1801,18678,18679,18687],{},[1804,18680,18681,18683,18685],{},[1807,18682,2301],{},[1811,18684,3250],{},[1807,18686,2421],{},[1823,18688,15192],{"encoding":1825},[1788,18690,18692,18710],{"className":18691,"ariaHidden":1831},[1830],[1788,18693,18695,18698,18701,18704,18707],{"className":18694},[1835],[1788,18696],{"className":18697,"style":4190},[1839],[1788,18699,2301],{"className":18700},[1844,1845],[1788,18702],{"className":18703,"style":3029},[1850],[1788,18705,3250],{"className":18706},[3033],[1788,18708],{"className":18709,"style":3029},[1850],[1788,18711,18713,18716],{"className":18712},[1835],[1788,18714],{"className":18715,"style":3114},[1839],[1788,18717,2421],{"className":18718,"style":1846},[1844,1845]," 个线性无关的解，而 ",[1788,18721,18723,18769],{"className":18722},[1791],[1788,18724,18726],{"className":18725},[1795],[1797,18727,18728],{"xmlns":1799},[1801,18729,18730,18766],{},[1804,18731,18732,18738,18740,18746,18748,18750,18752,18754],{},[2881,18733,18734,18736],{},[1807,18735,8230],{},[1985,18737,2906],{},[1811,18739,2430],{"separator":1831},[2881,18741,18742,18744],{},[1807,18743,8230],{},[1985,18745,2896],{},[1811,18747,2430],{"separator":1831},[1811,18749,9241],{},[1971,18751,2433],{},[1811,18753,2430],{"separator":1831},[2881,18755,18756,18758],{},[1807,18757,8230],{},[1804,18759,18760,18762,18764],{},[1807,18761,2301],{},[1811,18763,3250],{},[1807,18765,2421],{},[1823,18767,18768],{"encoding":1825},"x_1,x_2,\\cdots,x_{n-r}",[1788,18770,18772],{"className":18771,"ariaHidden":1831},[1830],[1788,18773,18775,18779,18819,18822,18825,18865,18868,18871,18874,18877,18880,18883,18886],{"className":18774},[1835],[1788,18776],{"className":18777,"style":18778},[1839],"height:0.6389em;vertical-align:-0.2083em;",[1788,18780,18782,18785],{"className":18781},[1844],[1788,18783,8230],{"className":18784},[1844,1845],[1788,18786,18788],{"className":18787},[1875],[1788,18789,18791,18811],{"className":18790},[1879,2931],[1788,18792,18794,18808],{"className":18793},[1883],[1788,18795,18797],{"className":18796,"style":2938},[1887],[1788,18798,18799,18802],{"style":4072},[1788,18800],{"className":18801,"style":1895},[1894],[1788,18803,18805],{"className":18804},[1899,1900,1901,1902],[1788,18806,2906],{"className":18807},[1844,1902],[1788,18809,2958],{"className":18810},[2957],[1788,18812,18814],{"className":18813},[1883],[1788,18815,18817],{"className":18816,"style":2965},[1887],[1788,18818],{},[1788,18820,2430],{"className":18821},[2474],[1788,18823],{"className":18824,"style":2478},[1850],[1788,18826,18828,18831],{"className":18827},[1844],[1788,18829,8230],{"className":18830},[1844,1845],[1788,18832,18834],{"className":18833},[1875],[1788,18835,18837,18857],{"className":18836},[1879,2931],[1788,18838,18840,18854],{"className":18839},[1883],[1788,18841,18843],{"className":18842,"style":2938},[1887],[1788,18844,18845,18848],{"style":4072},[1788,18846],{"className":18847,"style":1895},[1894],[1788,18849,18851],{"className":18850},[1899,1900,1901,1902],[1788,18852,2896],{"className":18853},[1844,1902],[1788,18855,2958],{"className":18856},[2957],[1788,18858,18860],{"className":18859},[1883],[1788,18861,18863],{"className":18862,"style":2965},[1887],[1788,18864],{},[1788,18866,2430],{"className":18867},[2474],[1788,18869],{"className":18870,"style":2478},[1850],[1788,18872,9241],{"className":18873},[9480],[1788,18875],{"className":18876,"style":2478},[1850],[1788,18878],{"className":18879,"style":2478},[1850],[1788,18881,2430],{"className":18882},[2474],[1788,18884],{"className":18885,"style":2478},[1850],[1788,18887,18889,18892],{"className":18888},[1844],[1788,18890,8230],{"className":18891},[1844,1845],[1788,18893,18895],{"className":18894},[1875],[1788,18896,18898,18927],{"className":18897},[1879,2931],[1788,18899,18901,18924],{"className":18900},[1883],[1788,18902,18904],{"className":18903,"style":7301},[1887],[1788,18905,18906,18909],{"style":4072},[1788,18907],{"className":18908,"style":1895},[1894],[1788,18910,18912],{"className":18911},[1899,1900,1901,1902],[1788,18913,18915,18918,18921],{"className":18914},[1844,1902],[1788,18916,2301],{"className":18917},[1844,1845,1902],[1788,18919,3250],{"className":18920},[3033,1902],[1788,18922,2421],{"className":18923,"style":1846},[1844,1845,1902],[1788,18925,2958],{"className":18926},[2957],[1788,18928,18930],{"className":18929},[1883],[1788,18931,18933],{"className":18932,"style":7331},[1887],[1788,18934],{}," 刚好是 ",[1788,18937,18939,18958],{"className":18938},[1791],[1788,18940,18942],{"className":18941},[1795],[1797,18943,18944],{"xmlns":1799},[1801,18945,18946,18956],{},[1804,18947,18948,18950,18952,18954],{},[1807,18949,2290],{},[1807,18951,8230],{},[1811,18953,1813],{},[1985,18955,1987],{},[1823,18957,12804],{"encoding":1825},[1788,18959,18961,18982],{"className":18960,"ariaHidden":1831},[1830],[1788,18962,18964,18967,18970,18973,18976,18979],{"className":18963},[1835],[1788,18965],{"className":18966,"style":1840},[1839],[1788,18968,2290],{"className":18969},[1844,1845],[1788,18971,8230],{"className":18972},[1844,1845],[1788,18974],{"className":18975,"style":1851},[1850],[1788,18977,1813],{"className":18978},[1855],[1788,18980],{"className":18981,"style":1851},[1850],[1788,18983,18985,18988],{"className":18984},[1835],[1788,18986],{"className":18987,"style":4209},[1839],[1788,18989,1987],{"className":18990},[1844]," 的 ",[1788,18993,18995,19012],{"className":18994},[1791],[1788,18996,18998],{"className":18997},[1795],[1797,18999,19000],{"xmlns":1799},[1801,19001,19002,19010],{},[1804,19003,19004,19006,19008],{},[1807,19005,2301],{},[1811,19007,3250],{},[1807,19009,2421],{},[1823,19011,15192],{"encoding":1825},[1788,19013,19015,19033],{"className":19014,"ariaHidden":1831},[1830],[1788,19016,19018,19021,19024,19027,19030],{"className":19017},[1835],[1788,19019],{"className":19020,"style":4190},[1839],[1788,19022,2301],{"className":19023},[1844,1845],[1788,19025],{"className":19026,"style":3029},[1850],[1788,19028,3250],{"className":19029},[3033],[1788,19031],{"className":19032,"style":3029},[1850],[1788,19034,19036,19039],{"className":19035},[1835],[1788,19037],{"className":19038,"style":3114},[1839],[1788,19040,2421],{"className":19041,"style":1846},[1844,1845]," 个线性无关解，所以 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的组合系数是 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同理",[1091,20101,20103],{"id":20102},"八-对比记忆","八. 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矩阵 ",[1788,20179,20181,20194],{"className":20180},[1791],[1788,20182,20184],{"className":20183},[1795],[1797,20185,20186],{"xmlns":1799},[1801,20187,20188,20192],{},[1804,20189,20190],{},[1807,20191,2290],{},[1823,20193,2290],{"encoding":1825},[1788,20195,20197],{"className":20196,"ariaHidden":1831},[1830],[1788,20198,20200,20203],{"className":20199},[1835],[1788,20201],{"className":20202,"style":1840},[1839],[1788,20204,2290],{"className":20205},[1844,1845]," 的迹＝对角线元素之和，即",[1096,20208,20209],{},[1788,20210,20212,20262],{"className":20211},[1791],[1788,20213,20215],{"className":20214},[1795],[1797,20216,20217],{"xmlns":1799},[1801,20218,20219,20259],{},[1804,20220,20221,20223,20225,20227,20229,20231,20233,20249],{},[1807,20222,20133],{"mathvariant":1982},[1811,20224,6333],{},[1811,20226,1977],{"stretchy":1976},[1807,20228,2290],{},[1811,20230,1990],{"stretchy":1976},[1811,20232,1813],{},[20234,20235,20236,20239,20247],"msubsup",{},[1811,20237,20238],{},"∑",[1804,20240,20241,20243,20245],{},[1807,20242,4034],{},[1811,20244,1813],{},[1985,20246,2906],{},[1807,20248,2301],{},[2881,20250,20251,20253],{},[1807,20252,1105],{},[1804,20254,20255,20257],{},[1807,20256,4034],{},[1807,20258,4034],{},[1823,20260,20261],{"encoding":1825},"\\operatorname{tr}(A)=\\sum_{i=1}^{n}a_{ii}",[1788,20263,20265,20295],{"className":20264,"ariaHidden":1831},[1830],[1788,20266,20268,20271,20277,20280,20283,20286,20289,20292],{"className":20267},[1835],[1788,20269],{"className":20270,"style":2003},[1839],[1788,20272,20274],{"className":20273},[6407],[1788,20275,20133],{"className":20276},[1844,9267],[1788,20278,1977],{"className":20279},[2013],[1788,20281,2290],{"className":20282},[1844,1845],[1788,20284,1990],{"className":20285},[2079],[1788,20287],{"className":20288,"style":1851},[1850],[1788,20290,1813],{"className":20291},[1855],[1788,20293],{"className":20294,"style":1851},[1850],[1788,20296,20298,20302,20372,20375],{"className":20297},[1835],[1788,20299],{"className":20300,"style":20301},[1839],"height:1.104em;vertical-align:-0.2997em;",[1788,20303,20305,20311],{"className":20304},[6407],[1788,20306,20238],{"className":20307,"style":20310},[6407,20308,20309],"op-symbol","small-op","position:relative;top:0em;",[1788,20312,20314],{"className":20313},[1875],[1788,20315,20317,20363],{"className":20316},[1879,2931],[1788,20318,20320,20360],{"className":20319},[1883],[1788,20321,20324,20345],{"className":20322,"style":20323},[1887],"height:0.8043em;",[1788,20325,20327,20330],{"style":20326},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1788,20328],{"className":20329,"style":1895},[1894],[1788,20331,20333],{"className":20332},[1899,1900,1901,1902],[1788,20334,20336,20339,20342],{"className":20335},[1844,1902],[1788,20337,4034],{"className":20338},[1844,1845,1902],[1788,20340,1813],{"className":20341},[1855,1902],[1788,20343,2906],{"className":20344},[1844,1902],[1788,20346,20348,20351],{"style":20347},"top:-3.2029em;margin-right:0.05em;",[1788,20349],{"className":20350,"style":1895},[1894],[1788,20352,20354],{"className":20353},[1899,1900,1901,1902],[1788,20355,20357],{"className":20356},[1844,1902],[1788,20358,2301],{"className":20359},[1844,1845,1902],[1788,20361,2958],{"className":20362},[2957],[1788,20364,20366],{"className":20365},[1883],[1788,20367,20370],{"className":20368,"style":20369},[1887],"height:0.2997em;",[1788,20371],{},[1788,20373],{"className":20374,"style":2478},[1850],[1788,20376,20378,20381],{"className":20377},[1844],[1788,20379,1105],{"className":20380},[1844,1845],[1788,20382,20384],{"className":20383},[1875],[1788,20385,20387,20411],{"className":20386},[1879,2931],[1788,20388,20390,20408],{"className":20389},[1883],[1788,20391,20393],{"className":20392,"style":4069},[1887],[1788,20394,20395,20398],{"style":4072},[1788,20396],{"className":20397,"style":1895},[1894],[1788,20399,20401],{"className":20400},[1899,1900,1901,1902],[1788,20402,20404],{"className":20403},[1844,1902],[1788,20405,20407],{"className":20406},[1844,1845,1902],"ii",[1788,20409,2958],{"className":20410},[2957],[1788,20412,20414],{"className":20413},[1883],[1788,20415,20417],{"className":20416,"style":2965},[1887],[1788,20418],{},[1780,20420,20422],{"id":20421},"_2-秩为1的矩阵","2. 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都是 ",[1788,20618,20620,20633],{"className":20619},[1791],[1788,20621,20623],{"className":20622},[1795],[1797,20624,20625],{"xmlns":1799},[1801,20626,20627,20631],{},[1804,20628,20629],{},[1807,20630,2301],{},[1823,20632,2301],{"encoding":1825},[1788,20634,20636],{"className":20635,"ariaHidden":1831},[1830],[1788,20637,20639,20642],{"className":20638},[1835],[1788,20640],{"className":20641,"style":3114},[1839],[1788,20643,2301],{"className":20644},[1844,1845]," 维非零列向量），其特征值为",[1096,20647,20648],{},[1788,20649,20651,20757],{"className":20650},[1791],[1788,20652,20654],{"className":20653},[1795],[1797,20655,20656],{"xmlns":1799},[1801,20657,20658,20754],{},[1804,20659,20660,20667,20669,20675,20677,20679,20681,20693,20695,20697,20699,20702,20708,20710,20724,20734,20736,20742,20744,20746,20752],{},[2881,20661,20662,20665],{},[1807,20663,20664],{},"λ",[1985,20666,2906],{},[1811,20668,1813],{},[2881,20670,20671,20673],{},[1807,20672,20664],{},[1985,20674,2896],{},[1811,20676,1813],{},[1811,20678,9241],{},[1811,20680,1813],{},[2881,20682,20683,20685],{},[1807,20684,20664],{},[1804,20686,20687,20689,20691],{},[1807,20688,2301],{},[1811,20690,3250],{},[1985,20692,2906],{},[1811,20694,1813],{},[1985,20696,1987],{},[1811,20698,2430],{"separator":1831},[1850,20700],{"width":20701},"2em",[2881,20703,20704,20706],{},[1807,20705,20664],{},[1807,20707,2301],{},[1811,20709,1813],{},[20234,20711,20712,20714,20722],{},[1811,20713,20238],{},[1804,20715,20716,20718,20720],{},[1807,20717,4034],{},[1811,20719,1813],{},[1985,20721,2906],{},[1807,20723,2301],{},[2881,20725,20726,20728],{},[1807,20727,1105],{},[1804,20729,20730,20732],{},[1807,20731,4034],{},[1807,20733,4034],{},[1811,20735,1813],{},[1815,20737,20738,20740],{},[1807,20739,2850],{},[1807,20741,1821],{},[1807,20743,3101],{},[1811,20745,1813],{},[1815,20747,20748,20750],{},[1807,20749,3101],{},[1807,20751,1821],{},[1807,20753,2850],{},[1823,20755,20756],{"encoding":1825},"\\lambda_1=\\lambda_2=\\cdots=\\lambda_{n-1}=0,\\qquad \\lambda_n=\\sum_{i=1}^{n}a_{ii}=\\beta^{T}\\alpha=\\alpha^{T}\\beta",[1788,20758,20760,20815,20870,20888,20952,21020,21144,21194],{"className":20759,"ariaHidden":1831},[1830],[1788,20761,20763,20766,20806,20809,20812],{"className":20762},[1835],[1788,20764],{"className":20765,"style":17730},[1839],[1788,20767,20769,20772],{"className":20768},[1844],[1788,20770,20664],{"className":20771},[1844,1845],[1788,20773,20775],{"className":20774},[1875],[1788,20776,20778,20798],{"className":20777},[1879,2931],[1788,20779,20781,20795],{"className":20780},[1883],[1788,20782,20784],{"className":20783,"style":2938},[1887],[1788,20785,20786,20789],{"style":4072},[1788,20787],{"className":20788,"style":1895},[1894],[1788,20790,20792],{"className":20791},[1899,1900,1901,1902],[1788,20793,2906],{"className":20794},[1844,1902],[1788,20796,2958],{"className":20797},[2957],[1788,20799,20801],{"className":20800},[1883],[1788,20802,20804],{"className":20803,"style":2965},[1887],[1788,20805],{},[1788,20807],{"className":20808,"style":1851},[1850],[1788,20810,1813],{"className":20811},[1855],[1788,20813],{"className":20814,"style":1851},[1850],[1788,20816,20818,20821,20861,20864,20867],{"className":20817},[1835],[1788,20819],{"className":20820,"style":17730},[1839],[1788,20822,20824,20827],{"className":20823},[1844],[1788,20825,20664],{"className":20826},[1844,1845],[1788,20828,20830],{"className":20829},[1875],[1788,20831,20833,20853],{"className":20832},[1879,2931],[1788,20834,20836,20850],{"className":20835},[1883],[1788,20837,20839],{"className":20838,"style":2938},[1887],[1788,20840,20841,20844],{"style":4072},[1788,20842],{"className":20843,"style":1895},[1894],[1788,20845,20847],{"className":20846},[1899,1900,1901,1902],[1788,20848,2896],{"className":20849},[1844,1902],[1788,20851,2958],{"className":20852},[2957],[1788,20854,20856],{"className":20855},[1883],[1788,20857,20859],{"className":20858,"style":2965},[1887],[1788,20860],{},[1788,20862],{"className":20863,"style":1851},[1850],[1788,20865,1813],{"className":20866},[1855],[1788,20868],{"className":20869,"style":1851},[1850],[1788,20871,20873,20876,20879,20882,20885],{"className":20872},[1835],[1788,20874],{"className":20875,"style":12901},[1839],[1788,20877,9241],{"className":20878},[9480],[1788,20880],{"className":20881,"style":1851},[1850],[1788,20883,1813],{"className":20884},[1855],[1788,20886],{"className":20887,"style":1851},[1850],[1788,20889,20891,20894,20943,20946,20949],{"className":20890},[1835],[1788,20892],{"className":20893,"style":19331},[1839],[1788,20895,20897,20900],{"className":20896},[1844],[1788,20898,20664],{"className":20899},[1844,1845],[1788,20901,20903],{"className":20902},[1875],[1788,20904,20906,20935],{"className":20905},[1879,2931],[1788,20907,20909,20932],{"className":20908},[1883],[1788,20910,20912],{"className":20911,"style":2938},[1887],[1788,20913,20914,20917],{"style":4072},[1788,20915],{"className":20916,"style":1895},[1894],[1788,20918,20920],{"className":20919},[1899,1900,1901,1902],[1788,20921,20923,20926,20929],{"className":20922},[1844,1902],[1788,20924,2301],{"className":20925},[1844,1845,1902],[1788,20927,3250],{"className":20928},[3033,1902],[1788,20930,2906],{"className":20931},[1844,1902],[1788,20933,2958],{"className":20934},[2957],[1788,20936,20938],{"className":20937},[1883],[1788,20939,20941],{"className":20940,"style":7331},[1887],[1788,20942],{},[1788,20944],{"className":20945,"style":1851},[1850],[1788,20947,1813],{"className":20948},[1855],[1788,20950],{"className":20951,"style":1851},[1850],[1788,20953,20955,20958,20961,20964,20968,20971,21011,21014,21017],{"className":20954},[1835],[1788,20956],{"className":20957,"style":2041},[1839],[1788,20959,1987],{"className":20960},[1844],[1788,20962,2430],{"className":20963},[2474],[1788,20965],{"className":20966,"style":20967},[1850],"margin-right:2em;",[1788,20969],{"className":20970,"style":2478},[1850],[1788,20972,20974,20977],{"className":20973},[1844],[1788,20975,20664],{"className":20976},[1844,1845],[1788,20978,20980],{"className":20979},[1875],[1788,20981,20983,21003],{"className":20982},[1879,2931],[1788,20984,20986,21000],{"className":20985},[1883],[1788,20987,20989],{"className":20988,"style":17879},[1887],[1788,20990,20991,20994],{"style":4072},[1788,20992],{"className":20993,"style":1895},[1894],[1788,20995,20997],{"className":20996},[1899,1900,1901,1902],[1788,20998,2301],{"className":20999},[1844,1845,1902],[1788,21001,2958],{"className":21002},[2957],[1788,21004,21006],{"className":21005},[1883],[1788,21007,21009],{"className":21008,"style":2965},[1887],[1788,21010],{},[1788,21012],{"className":21013,"style":1851},[1850],[1788,21015,1813],{"className":21016},[1855],[1788,21018],{"className":21019,"style":1851},[1850],[1788,21021,21023,21026,21089,21092,21135,21138,21141],{"className":21022},[1835],[1788,21024],{"className":21025,"style":20301},[1839],[1788,21027,21029,21032],{"className":21028},[6407],[1788,21030,20238],{"className":21031,"style":20310},[6407,20308,20309],[1788,21033,21035],{"className":21034},[1875],[1788,21036,21038,21081],{"className":21037},[1879,2931],[1788,21039,21041,21078],{"className":21040},[1883],[1788,21042,21044,21064],{"className":21043,"style":20323},[1887],[1788,21045,21046,21049],{"style":20326},[1788,21047],{"className":21048,"style":1895},[1894],[1788,21050,21052],{"className":21051},[1899,1900,1901,1902],[1788,21053,21055,21058,21061],{"className":21054},[1844,1902],[1788,21056,4034],{"className":21057},[1844,1845,1902],[1788,21059,1813],{"className":21060},[1855,1902],[1788,21062,2906],{"className":21063},[1844,1902],[1788,21065,21066,21069],{"style":20347},[1788,21067],{"className":21068,"style":1895},[1894],[1788,21070,21072],{"className":21071},[1899,1900,1901,1902],[1788,21073,21075],{"className":21074},[1844,1902],[1788,21076,2301],{"className":21077},[1844,1845,1902],[1788,21079,2958],{"className":21080},[2957],[1788,21082,21084],{"className":21083},[1883],[1788,21085,21087],{"className":21086,"style":20369},[1887],[1788,21088],{},[1788,21090],{"className":21091,"style":2478},[1850],[1788,21093,21095,21098],{"className":21094},[1844],[1788,21096,1105],{"className":21097},[1844,1845],[1788,21099,21101],{"className":21100},[1875],[1788,21102,21104,21127],{"className":21103},[1879,2931],[1788,21105,21107,21124],{"className":21106},[1883],[1788,21108,21110],{"className":21109,"style":4069},[1887],[1788,21111,21112,21115],{"style":4072},[1788,21113],{"className":21114,"style":1895},[1894],[1788,21116,21118],{"className":21117},[1899,1900,1901,1902],[1788,21119,21121],{"className":21120},[1844,1902],[1788,21122,20407],{"className":21123},[1844,1845,1902],[1788,21125,2958],{"className":21126},[2957],[1788,21128,21130],{"className":21129},[1883],[1788,21131,21133],{"className":21132,"style":2965},[1887],[1788,21134],{},[1788,21136],{"className":21137,"style":1851},[1850],[1788,21139,1813],{"className":21140},[1855],[1788,21142],{"className":21143,"style":1851},[1850],[1788,21145,21147,21150,21182,21185,21188,21191],{"className":21146},[1835],[1788,21148],{"className":21149,"style":20537},[1839],[1788,21151,21153,21156],{"className":21152},[1844],[1788,21154,2850],{"className":21155,"style":2866},[1844,1845],[1788,21157,21159],{"className":21158},[1875],[1788,21160,21162],{"className":21161},[1879],[1788,21163,21165],{"className":21164},[1883],[1788,21166,21168],{"className":21167,"style":1865},[1887],[1788,21169,21170,21173],{"style":1890},[1788,21171],{"className":21172,"style":1895},[1894],[1788,21174,21176],{"className":21175},[1899,1900,1901,1902],[1788,21177,21179],{"className":21178},[1844,1902],[1788,21180,1821],{"className":21181,"style":1909},[1844,1845,1902],[1788,21183,3101],{"className":21184,"style":3118},[1844,1845],[1788,21186],{"className":21187,"style":1851},[1850],[1788,21189,1813],{"className":21190},[1855],[1788,21192],{"className":21193,"style":1851},[1850],[1788,21195,21197,21200,21232],{"className":21196},[1835],[1788,21198],{"className":21199,"style":20537},[1839],[1788,21201,21203,21206],{"className":21202},[1844],[1788,21204,3101],{"className":21205,"style":3118},[1844,1845],[1788,21207,21209],{"className":21208},[1875],[1788,21210,21212],{"className":21211},[1879],[1788,21213,21215],{"className":21214},[1883],[1788,21216,21218],{"className":21217,"style":1865},[1887],[1788,21219,21220,21223],{"style":1890},[1788,21221],{"className":21222,"style":1895},[1894],[1788,21224,21226],{"className":21225},[1899,1900,1901,1902],[1788,21227,21229],{"className":21228},[1844,1902],[1788,21230,1821],{"className":21231,"style":1909},[1844,1845,1902],[1788,21233,2850],{"className":21234,"style":2866},[1844,1845],[1096,21236,21237],{},[2114,21238],{"alt":21239,"src":21240},"秩为1的矩阵","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be1f593c8.png",[1780,21242,21244],{"id":21243},"_3","3.",[1096,21246,21247],{},[2114,21248],{"alt":21249,"src":21250},"对比记忆（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be204a814.png",[1096,21252,21253],{},[1099,21254,21255],{},"例题1：",[1096,21257,21258],{},[2114,21259],{"alt":21260,"src":21261},"对比记忆例题1","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2066a1e.png",[1096,21263,21264],{},[1099,21265,21266],{},"例题2：",[1096,21268,21269],{},[2114,21270],{"alt":21271,"src":21272},"对比记忆例题2","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be20bc1f4.png",[1091,21274,21276],{"id":21275},"九-相似与正交","九. 相似与正交",[1096,21278,21279,21280,21308,21309,9061,21337,21438,21439,21467,21468,21496,21497,2389],{},"存在 ",[1788,21281,21283,21296],{"className":21282},[1791],[1788,21284,21286],{"className":21285},[1795],[1797,21287,21288],{"xmlns":1799},[1801,21289,21290,21294],{},[1804,21291,21292],{},[1807,21293,2301],{},[1823,21295,2301],{"encoding":1825},[1788,21297,21299],{"className":21298,"ariaHidden":1831},[1830],[1788,21300,21302,21305],{"className":21301},[1835],[1788,21303],{"className":21304,"style":3114},[1839],[1788,21306,2301],{"className":21307},[1844,1845]," 阶可逆矩阵 ",[1788,21310,21312,21325],{"className":21311},[1791],[1788,21313,21315],{"className":21314},[1795],[1797,21316,21317],{"xmlns":1799},[1801,21318,21319,21323],{},[1804,21320,21321],{},[1807,21322,7667],{},[1823,21324,7667],{"encoding":1825},[1788,21326,21328],{"className":21327,"ariaHidden":1831},[1830],[1788,21329,21331,21334],{"className":21330},[1835],[1788,21332],{"className":21333,"style":1840},[1839],[1788,21335,7667],{"className":21336,"style":1909},[1844,1845],[1788,21338,21340,21370],{"className":21339},[1791],[1788,21341,21343],{"className":21342},[1795],[1797,21344,21345],{"xmlns":1799},[1801,21346,21347,21367],{},[1804,21348,21349,21359,21361,21363,21365],{},[1815,21350,21351,21353],{},[1807,21352,7667],{},[1804,21354,21355,21357],{},[1811,21356,3250],{},[1985,21358,2906],{},[1807,21360,2290],{},[1807,21362,7667],{},[1811,21364,1813],{},[1807,21366,3841],{},[1823,21368,21369],{"encoding":1825},"P^{-1}AP=B",[1788,21371,21373,21429],{"className":21372,"ariaHidden":1831},[1830],[1788,21374,21376,21379,21414,21417,21420,21423,21426],{"className":21375},[1835],[1788,21377],{"className":21378,"style":3265},[1839],[1788,21380,21382,21385],{"className":21381},[1844],[1788,21383,7667],{"className":21384,"style":1909},[1844,1845],[1788,21386,21388],{"className":21387},[1875],[1788,21389,21391],{"className":21390},[1879],[1788,21392,21394],{"className":21393},[1883],[1788,21395,21397],{"className":21396,"style":3265},[1887],[1788,21398,21399,21402],{"style":1890},[1788,21400],{"className":21401,"style":1895},[1894],[1788,21403,21405],{"className":21404},[1899,1900,1901,1902],[1788,21406,21408,21411],{"className":21407},[1844,1902],[1788,21409,3250],{"className":21410},[1844,1902],[1788,21412,2906],{"className":21413},[1844,1902],[1788,21415,2290],{"className":21416},[1844,1845],[1788,21418,7667],{"className":21419,"style":1909},[1844,1845],[1788,21421],{"className":21422,"style":1851},[1850],[1788,21424,1813],{"className":21425},[1855],[1788,21427],{"className":21428,"style":1851},[1850],[1788,21430,21432,21435],{"className":21431},[1835],[1788,21433],{"className":21434,"style":1840},[1839],[1788,21436,3841],{"className":21437,"style":3866},[1844,1845],"，则称 ",[1788,21440,21442,21455],{"className":21441},[1791],[1788,21443,21445],{"className":21444},[1795],[1797,21446,21447],{"xmlns":1799},[1801,21448,21449,21453],{},[1804,21450,21451],{},[1807,21452,2290],{},[1823,21454,2290],{"encoding":1825},[1788,21456,21458],{"className":21457,"ariaHidden":1831},[1830],[1788,21459,21461,21464],{"className":21460},[1835],[1788,21462],{"className":21463,"style":1840},[1839],[1788,21465,2290],{"className":21466},[1844,1845]," 相似于 ",[1788,21469,21471,21484],{"className":21470},[1791],[1788,21472,21474],{"className":21473},[1795],[1797,21475,21476],{"xmlns":1799},[1801,21477,21478,21482],{},[1804,21479,21480],{},[1807,21481,3841],{},[1823,21483,3841],{"encoding":1825},[1788,21485,21487],{"className":21486,"ariaHidden":1831},[1830],[1788,21488,21490,21493],{"className":21489},[1835],[1788,21491],{"className":21492,"style":1840},[1839],[1788,21494,3841],{"className":21495,"style":3866},[1844,1845],"，记为 ",[1788,21498,21500,21518],{"className":21499},[1791],[1788,21501,21503],{"className":21502},[1795],[1797,21504,21505],{"xmlns":1799},[1801,21506,21507,21515],{},[1804,21508,21509,21511,21513],{},[1807,21510,2290],{},[1811,21512,6081],{},[1807,21514,3841],{},[1823,21516,21517],{"encoding":1825},"A\\sim B",[1788,21519,21521,21539],{"className":21520,"ariaHidden":1831},[1830],[1788,21522,21524,21527,21530,21533,21536],{"className":21523},[1835],[1788,21525],{"className":21526,"style":1840},[1839],[1788,21528,2290],{"className":21529},[1844,1845],[1788,21531],{"className":21532,"style":1851},[1850],[1788,21534,6081],{"className":21535},[1855],[1788,21537],{"className":21538,"style":1851},[1850],[1788,21540,21542,21545],{"className":21541},[1835],[1788,21543],{"className":21544,"style":1840},[1839],[1788,21546,3841],{"className":21547,"style":3866},[1844,1845],[1912,21549,21550,21603],{},[1096,21551,7227,21552,21602],{},[1788,21553,21555,21572],{"className":21554},[1791],[1788,21556,21558],{"className":21557},[1795],[1797,21559,21560],{"xmlns":1799},[1801,21561,21562,21570],{},[1804,21563,21564,21566,21568],{},[1807,21565,2290],{},[1811,21567,6081],{},[1807,21569,3841],{},[1823,21571,21517],{"encoding":1825},[1788,21573,21575,21593],{"className":21574,"ariaHidden":1831},[1830],[1788,21576,21578,21581,21584,21587,21590],{"className":21577},[1835],[1788,21579],{"className":21580,"style":1840},[1839],[1788,21582,2290],{"className":21583},[1844,1845],[1788,21585],{"className":21586,"style":1851},[1850],[1788,21588,6081],{"className":21589},[1855],[1788,21591],{"className":21592,"style":1851},[1850],[1788,21594,21596,21599],{"className":21595},[1835],[1788,21597],{"className":21598,"style":1840},[1839],[1788,21600,3841],{"className":21601,"style":3866},[1844,1845],"，则",[1096,21604,6300,21605,21676,21677,21757,21758,11098,21849,10952,21983,22108,22109,22244,22245,22286],{},[1788,21606,21608,21634],{"className":21607},[1791],[1788,21609,21611],{"className":21610},[1795],[1797,21612,21613],{"xmlns":1799},[1801,21614,21615,21631],{},[1804,21616,21617,21619,21621,21623,21625,21627,21629],{},[1807,21618,2285],{"mathvariant":1982},[1807,21620,2290],{},[1807,21622,2285],{"mathvariant":1982},[1811,21624,1813],{},[1807,21626,2285],{"mathvariant":1982},[1807,21628,3841],{},[1807,21630,2285],{"mathvariant":1982},[1823,21632,21633],{"encoding":1825},"|A|=|B|",[1788,21635,21637,21661],{"className":21636,"ariaHidden":1831},[1830],[1788,21638,21640,21643,21646,21649,21652,21655,21658],{"className":21639},[1835],[1788,21641],{"className":21642,"style":2003},[1839],[1788,21644,2285],{"className":21645},[1844],[1788,21647,2290],{"className":21648},[1844,1845],[1788,21650,2285],{"className":21651},[1844],[1788,21653],{"className":21654,"style":1851},[1850],[1788,21656,1813],{"className":21657},[1855],[1788,21659],{"className":21660,"style":1851},[1850],[1788,21662,21664,21667,21670,21673],{"className":21663},[1835],[1788,21665],{"className":21666,"style":2003},[1839],[1788,21668,2285],{"className":21669},[1844],[1788,21671,3841],{"className":21672,"style":3866},[1844,1845],[1788,21674,2285],{"className":21675},[1844],"\n② ",[1788,21678,21680,21709],{"className":21679},[1791],[1788,21681,21683],{"className":21682},[1795],[1797,21684,21685],{"xmlns":1799},[1801,21686,21687,21707],{},[1804,21688,21689,21691,21693,21695,21697,21699,21701,21703,21705],{},[1807,21690,2421],{},[1811,21692,1977],{"stretchy":1976},[1807,21694,2290],{},[1811,21696,1990],{"stretchy":1976},[1811,21698,1813],{},[1807,21700,2421],{},[1811,21702,1977],{"stretchy":1976},[1807,21704,3841],{},[1811,21706,1990],{"stretchy":1976},[1823,21708,8970],{"encoding":1825},[1788,21710,21712,21739],{"className":21711,"ariaHidden":1831},[1830],[1788,21713,21715,21718,21721,21724,21727,21730,21733,21736],{"className":21714},[1835],[1788,21716],{"className":21717,"style":2003},[1839],[1788,21719,2421],{"className":21720,"style":1846},[1844,1845],[1788,21722,1977],{"className":21723},[2013],[1788,21725,2290],{"className":21726},[1844,1845],[1788,21728,1990],{"className":21729},[2079],[1788,21731],{"className":21732,"style":1851},[1850],[1788,21734,1813],{"className":21735},[1855],[1788,21737],{"className":21738,"style":1851},[1850],[1788,21740,21742,21745,21748,21751,21754],{"className":21741},[1835],[1788,21743],{"className":21744,"style":2003},[1839],[1788,21746,2421],{"className":21747,"style":1846},[1844,1845],[1788,21749,1977],{"className":21750},[2013],[1788,21752,3841],{"className":21753,"style":3866},[1844,1845],[1788,21755,1990],{"className":21756},[2079],"\n③ ",[1788,21759,21761,21795],{"className":21760},[1791],[1788,21762,21764],{"className":21763},[1795],[1797,21765,21766],{"xmlns":1799},[1801,21767,21768,21792],{},[1804,21769,21770,21772,21774,21776,21778,21780,21782,21784,21786,21788,21790],{},[1807,21771,20133],{"mathvariant":1982},[1811,21773,6333],{},[1811,21775,1977],{"stretchy":1976},[1807,21777,2290],{},[1811,21779,1990],{"stretchy":1976},[1811,21781,1813],{},[1807,21783,20133],{"mathvariant":1982},[1811,21785,6333],{},[1811,21787,1977],{"stretchy":1976},[1807,21789,3841],{},[1811,21791,1990],{"stretchy":1976},[1823,21793,21794],{"encoding":1825},"\\operatorname{tr}(A)=\\operatorname{tr}(B)",[1788,21796,21798,21828],{"className":21797,"ariaHidden":1831},[1830],[1788,21799,21801,21804,21810,21813,21816,21819,21822,21825],{"className":21800},[1835],[1788,21802],{"className":21803,"style":2003},[1839],[1788,21805,21807],{"className":21806},[6407],[1788,21808,20133],{"className":21809},[1844,9267],[1788,21811,1977],{"className":21812},[2013],[1788,21814,2290],{"className":21815},[1844,1845],[1788,21817,1990],{"className":21818},[2079],[1788,21820],{"className":21821,"style":1851},[1850],[1788,21823,1813],{"className":21824},[1855],[1788,21826],{"className":21827,"style":1851},[1850],[1788,21829,21831,21834,21840,21843,21846],{"className":21830},[1835],[1788,21832],{"className":21833,"style":2003},[1839],[1788,21835,21837],{"className":21836},[6407],[1788,21838,20133],{"className":21839},[1844,9267],[1788,21841,1977],{"className":21842},[2013],[1788,21844,3841],{"className":21845,"style":3866},[1844,1845],[1788,21847,1990],{"className":21848},[2079],[1788,21850,21852,21878],{"className":21851},[1791],[1788,21853,21855],{"className":21854},[1795],[1797,21856,21857],{"xmlns":1799},[1801,21858,21859,21875],{},[1804,21860,21861,21867,21869],{},[2881,21862,21863,21865],{},[1807,21864,20664],{},[1807,21866,2290],{},[1811,21868,1813],{},[2881,21870,21871,21873],{},[1807,21872,20664],{},[1807,21874,3841],{},[1823,21876,21877],{"encoding":1825},"\\lambda_A=\\lambda_B",[1788,21879,21881,21937],{"className":21880,"ariaHidden":1831},[1830],[1788,21882,21884,21887,21928,21931,21934],{"className":21883},[1835],[1788,21885],{"className":21886,"style":17730},[1839],[1788,21888,21890,21893],{"className":21889},[1844],[1788,21891,20664],{"className":21892},[1844,1845],[1788,21894,21896],{"className":21895},[1875],[1788,21897,21899,21920],{"className":21898},[1879,2931],[1788,21900,21902,21917],{"className":21901},[1883],[1788,21903,21906],{"className":21904,"style":21905},[1887],"height:0.3283em;",[1788,21907,21908,21911],{"style":4072},[1788,21909],{"className":21910,"style":1895},[1894],[1788,21912,21914],{"className":21913},[1899,1900,1901,1902],[1788,21915,2290],{"className":21916},[1844,1845,1902],[1788,21918,2958],{"className":21919},[2957],[1788,21921,21923],{"className":21922},[1883],[1788,21924,21926],{"className":21925,"style":2965},[1887],[1788,21927],{},[1788,21929],{"className":21930,"style":1851},[1850],[1788,21932,1813],{"className":21933},[1855],[1788,21935],{"className":21936,"style":1851},[1850],[1788,21938,21940,21943],{"className":21939},[1835],[1788,21941],{"className":21942,"style":17730},[1839],[1788,21944,21946,21949],{"className":21945},[1844],[1788,21947,20664],{"className":21948},[1844,1845],[1788,21950,21952],{"className":21951},[1875],[1788,21953,21955,21975],{"className":21954},[1879,2931],[1788,21956,21958,21972],{"className":21957},[1883],[1788,21959,21961],{"className":21960,"style":21905},[1887],[1788,21962,21963,21966],{"style":4072},[1788,21964],{"className":21965,"style":1895},[1894],[1788,21967,21969],{"className":21968},[1899,1900,1901,1902],[1788,21970,3841],{"className":21971,"style":3866},[1844,1845,1902],[1788,21973,2958],{"className":21974},[2957],[1788,21976,21978],{"className":21977},[1883],[1788,21979,21981],{"className":21980,"style":2965},[1887],[1788,21982],{},[1788,21984,21986,22024],{"className":21985},[1791],[1788,21987,21989],{"className":21988},[1795],[1797,21990,21991],{"xmlns":1799},[1801,21992,21993,22021],{},[1804,21994,21995,21997,21999,22001,22003,22005,22007,22009,22011,22013,22015,22017,22019],{},[1807,21996,2285],{"mathvariant":1982},[1807,21998,20664],{},[1807,22000,3192],{},[1811,22002,3250],{},[1807,22004,2290],{},[1807,22006,2285],{"mathvariant":1982},[1811,22008,1813],{},[1807,22010,2285],{"mathvariant":1982},[1807,22012,20664],{},[1807,22014,3192],{},[1811,22016,3250],{},[1807,22018,3841],{},[1807,22020,2285],{"mathvariant":1982},[1823,22022,22023],{"encoding":1825},"|\\lambda E-A|=|\\lambda E-B|",[1788,22025,22027,22051,22072,22096],{"className":22026,"ariaHidden":1831},[1830],[1788,22028,22030,22033,22036,22039,22042,22045,22048],{"className":22029},[1835],[1788,22031],{"className":22032,"style":2003},[1839],[1788,22034,2285],{"className":22035},[1844],[1788,22037,20664],{"className":22038},[1844,1845],[1788,22040,3192],{"className":22041,"style":3222},[1844,1845],[1788,22043],{"className":22044,"style":3029},[1850],[1788,22046,3250],{"className":22047},[3033],[1788,22049],{"className":22050,"style":3029},[1850],[1788,22052,22054,22057,22060,22063,22066,22069],{"className":22053},[1835],[1788,22055],{"className":22056,"style":2003},[1839],[1788,22058,2290],{"className":22059},[1844,1845],[1788,22061,2285],{"className":22062},[1844],[1788,22064],{"className":22065,"style":1851},[1850],[1788,22067,1813],{"className":22068},[1855],[1788,22070],{"className":22071,"style":1851},[1850],[1788,22073,22075,22078,22081,22084,22087,22090,22093],{"className":22074},[1835],[1788,22076],{"className":22077,"style":2003},[1839],[1788,22079,2285],{"className":22080},[1844],[1788,22082,20664],{"className":22083},[1844,1845],[1788,22085,3192],{"className":22086,"style":3222},[1844,1845],[1788,22088],{"className":22089,"style":3029},[1850],[1788,22091,3250],{"className":22092},[3033],[1788,22094],{"className":22095,"style":3029},[1850],[1788,22097,22099,22102,22105],{"className":22098},[1835],[1788,22100],{"className":22101,"style":2003},[1839],[1788,22103,3841],{"className":22104,"style":3866},[1844,1845],[1788,22106,2285],{"className":22107},[1844],"\n⑤ ",[1788,22110,22112,22154],{"className":22111},[1791],[1788,22113,22115],{"className":22114},[1795],[1797,22116,22117],{"xmlns":1799},[1801,22118,22119,22151],{},[1804,22120,22121,22123,22125,22127,22129,22131,22133,22135,22137,22139,22141,22143,22145,22147,22149],{},[1807,22122,2421],{},[1811,22124,1977],{"stretchy":1976},[1807,22126,20664],{},[1807,22128,3192],{},[1811,22130,3250],{},[1807,22132,2290],{},[1811,22134,1990],{"stretchy":1976},[1811,22136,1813],{},[1807,22138,2421],{},[1811,22140,1977],{"stretchy":1976},[1807,22142,20664],{},[1807,22144,3192],{},[1811,22146,3250],{},[1807,22148,3841],{},[1811,22150,1990],{"stretchy":1976},[1823,22152,22153],{"encoding":1825},"r(\\lambda E-A)=r(\\lambda E-B)",[1788,22155,22157,22184,22205,22232],{"className":22156,"ariaHidden":1831},[1830],[1788,22158,22160,22163,22166,22169,22172,22175,22178,22181],{"className":22159},[1835],[1788,22161],{"className":22162,"style":2003},[1839],[1788,22164,2421],{"className":22165,"style":1846},[1844,1845],[1788,22167,1977],{"className":22168},[2013],[1788,22170,20664],{"className":22171},[1844,1845],[1788,22173,3192],{"className":22174,"style":3222},[1844,1845],[1788,22176],{"className":22177,"style":3029},[1850],[1788,22179,3250],{"className":22180},[3033],[1788,22182],{"className":22183,"style":3029},[1850],[1788,22185,22187,22190,22193,22196,22199,22202],{"className":22186},[1835],[1788,22188],{"className":22189,"style":2003},[1839],[1788,22191,2290],{"className":22192},[1844,1845],[1788,22194,1990],{"className":22195},[2079],[1788,22197],{"className":22198,"style":1851},[1850],[1788,22200,1813],{"className":22201},[1855],[1788,22203],{"className":22204,"style":1851},[1850],[1788,22206,22208,22211,22214,22217,22220,22223,22226,22229],{"className":22207},[1835],[1788,22209],{"className":22210,"style":2003},[1839],[1788,22212,2421],{"className":22213,"style":1846},[1844,1845],[1788,22215,1977],{"className":22216},[2013],[1788,22218,20664],{"className":22219},[1844,1845],[1788,22221,3192],{"className":22222,"style":3222},[1844,1845],[1788,22224],{"className":22225,"style":3029},[1850],[1788,22227,3250],{"className":22228},[3033],[1788,22230],{"className":22231,"style":3029},[1850],[1788,22233,22235,22238,22241],{"className":22234},[1835],[1788,22236],{"className":22237,"style":2003},[1839],[1788,22239,3841],{"className":22240,"style":3866},[1844,1845],[1788,22242,1990],{"className":22243},[2079],"\n⑥ ",[1788,22246,22248,22265],{"className":22247},[1791],[1788,22249,22251],{"className":22250},[1795],[1797,22252,22253],{"xmlns":1799},[1801,22254,22255,22263],{},[1804,22256,22257,22259,22261],{},[1807,22258,2290],{},[1811,22260,2430],{"separator":1831},[1807,22262,3841],{},[1823,22264,8906],{"encoding":1825},[1788,22266,22268],{"className":22267,"ariaHidden":1831},[1830],[1788,22269,22271,22274,22277,22280,22283],{"className":22270},[1835],[1788,22272],{"className":22273,"style":7685},[1839],[1788,22275,2290],{"className":22276},[1844,1845],[1788,22278,2430],{"className":22279},[2474],[1788,22281],{"className":22282,"style":2478},[1850],[1788,22284,3841],{"className":22285,"style":3866},[1844,1845]," 各阶主子式之和分别相同",[1096,22288,22289],{},[2114,22290],{"alt":22291,"src":22292},"相似的性质","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be222816e.png",[1096,22294,22295,22296,8852,22324,22352,22353,22394,22395,22436,22437,12917],{},"也就是说，",[1788,22297,22299,22312],{"className":22298},[1791],[1788,22300,22302],{"className":22301},[1795],[1797,22303,22304],{"xmlns":1799},[1801,22305,22306,22310],{},[1804,22307,22308],{},[1807,22309,2290],{},[1823,22311,2290],{"encoding":1825},[1788,22313,22315],{"className":22314,"ariaHidden":1831},[1830],[1788,22316,22318,22321],{"className":22317},[1835],[1788,22319],{"className":22320,"style":1840},[1839],[1788,22322,2290],{"className":22323},[1844,1845],[1788,22325,22327,22340],{"className":22326},[1791],[1788,22328,22330],{"className":22329},[1795],[1797,22331,22332],{"xmlns":1799},[1801,22333,22334,22338],{},[1804,22335,22336],{},[1807,22337,3841],{},[1823,22339,3841],{"encoding":1825},[1788,22341,22343],{"className":22342,"ariaHidden":1831},[1830],[1788,22344,22346,22349],{"className":22345},[1835],[1788,22347],{"className":22348,"style":1840},[1839],[1788,22350,3841],{"className":22351,"style":3866},[1844,1845]," 即使特征值相同，也不一定相似。但是如果 ",[1788,22354,22356,22373],{"className":22355},[1791],[1788,22357,22359],{"className":22358},[1795],[1797,22360,22361],{"xmlns":1799},[1801,22362,22363,22371],{},[1804,22364,22365,22367,22369],{},[1807,22366,2290],{},[1811,22368,2430],{"separator":1831},[1807,22370,3841],{},[1823,22372,8906],{"encoding":1825},[1788,22374,22376],{"className":22375,"ariaHidden":1831},[1830],[1788,22377,22379,22382,22385,22388,22391],{"className":22378},[1835],[1788,22380],{"className":22381,"style":7685},[1839],[1788,22383,2290],{"className":22384},[1844,1845],[1788,22386,2430],{"className":22387},[2474],[1788,22389],{"className":22390,"style":2478},[1850],[1788,22392,3841],{"className":22393,"style":3866},[1844,1845]," 都是实对称矩阵，那么特征值相同就一定相似（",[1788,22396,22398,22415],{"className":22397},[1791],[1788,22399,22401],{"className":22400},[1795],[1797,22402,22403],{"xmlns":1799},[1801,22404,22405,22413],{},[1804,22406,22407,22409,22411],{},[1807,22408,2290],{},[1811,22410,2430],{"separator":1831},[1807,22412,3841],{},[1823,22414,8906],{"encoding":1825},[1788,22416,22418],{"className":22417,"ariaHidden":1831},[1830],[1788,22419,22421,22424,22427,22430,22433],{"className":22420},[1835],[1788,22422],{"className":22423,"style":7685},[1839],[1788,22425,2290],{"className":22426},[1844,1845],[1788,22428,2430],{"className":22429},[2474],[1788,22431],{"className":22432,"style":2478},[1850],[1788,22434,3841],{"className":22435,"style":3866},[1844,1845]," 都能正交相似于同一个对角矩阵，由相似传递性得 ",[1788,22438,22440,22457],{"className":22439},[1791],[1788,22441,22443],{"className":22442},[1795],[1797,22444,22445],{"xmlns":1799},[1801,22446,22447,22455],{},[1804,22448,22449,22451,22453],{},[1807,22450,2290],{},[1811,22452,6081],{},[1807,22454,3841],{},[1823,22456,21517],{"encoding":1825},[1788,22458,22460,22478],{"className":22459,"ariaHidden":1831},[1830],[1788,22461,22463,22466,22469,22472,22475],{"className":22462},[1835],[1788,22464],{"className":22465,"style":1840},[1839],[1788,22467,2290],{"className":22468},[1844,1845],[1788,22470],{"className":22471,"style":1851},[1850],[1788,22473,6081],{"className":22474},[1855],[1788,22476],{"className":22477,"style":1851},[1850],[1788,22479,22481,22484],{"className":22480},[1835],[1788,22482],{"className":22483,"style":1840},[1839],[1788,22485,3841],{"className":22486,"style":3866},[1844,1845],[1096,22488,22489],{},[1099,22490,22491],{},"那么怎么判定矩阵相似呢？",[1912,22493,22494],{},[1096,22495,6300,22496,22499,22500,21308,22528,9061,22556,15080,22656,8935,22659,2080,22751,22801,22802,22831],{},[1099,22497,22498],{},"定义法","：存在 ",[1788,22501,22503,22516],{"className":22502},[1791],[1788,22504,22506],{"className":22505},[1795],[1797,22507,22508],{"xmlns":1799},[1801,22509,22510,22514],{},[1804,22511,22512],{},[1807,22513,2301],{},[1823,22515,2301],{"encoding":1825},[1788,22517,22519],{"className":22518,"ariaHidden":1831},[1830],[1788,22520,22522,22525],{"className":22521},[1835],[1788,22523],{"className":22524,"style":3114},[1839],[1788,22526,2301],{"className":22527},[1844,1845],[1788,22529,22531,22544],{"className":22530},[1791],[1788,22532,22534],{"className":22533},[1795],[1797,22535,22536],{"xmlns":1799},[1801,22537,22538,22542],{},[1804,22539,22540],{},[1807,22541,7667],{},[1823,22543,7667],{"encoding":1825},[1788,22545,22547],{"className":22546,"ariaHidden":1831},[1830],[1788,22548,22550,22553],{"className":22549},[1835],[1788,22551],{"className":22552,"style":1840},[1839],[1788,22554,7667],{"className":22555,"style":1909},[1844,1845],[1788,22557,22559,22588],{"className":22558},[1791],[1788,22560,22562],{"className":22561},[1795],[1797,22563,22564],{"xmlns":1799},[1801,22565,22566,22586],{},[1804,22567,22568,22578,22580,22582,22584],{},[1815,22569,22570,22572],{},[1807,22571,7667],{},[1804,22573,22574,22576],{},[1811,22575,3250],{},[1985,22577,2906],{},[1807,22579,2290],{},[1807,22581,7667],{},[1811,22583,1813],{},[1807,22585,3841],{},[1823,22587,21369],{"encoding":1825},[1788,22589,22591,22647],{"className":22590,"ariaHidden":1831},[1830],[1788,22592,22594,22597,22632,22635,22638,22641,22644],{"className":22593},[1835],[1788,22595],{"className":22596,"style":3265},[1839],[1788,22598,22600,22603],{"className":22599},[1844],[1788,22601,7667],{"className":22602,"style":1909},[1844,1845],[1788,22604,22606],{"className":22605},[1875],[1788,22607,22609],{"className":22608},[1879],[1788,22610,22612],{"className":22611},[1883],[1788,22613,22615],{"className":22614,"style":3265},[1887],[1788,22616,22617,22620],{"style":1890},[1788,22618],{"className":22619,"style":1895},[1894],[1788,22621,22623],{"className":22622},[1899,1900,1901,1902],[1788,22624,22626,22629],{"className":22625},[1844,1902],[1788,22627,3250],{"className":22628},[1844,1902],[1788,22630,2906],{"className":22631},[1844,1902],[1788,22633,2290],{"className":22634},[1844,1845],[1788,22636,7667],{"className":22637,"style":1909},[1844,1845],[1788,22639],{"className":22640,"style":1851},[1850],[1788,22642,1813],{"className":22643},[1855],[1788,22645],{"className":22646,"style":1851},[1850],[1788,22648,22650,22653],{"className":22649},[1835],[1788,22651],{"className":22652,"style":1840},[1839],[1788,22654,3841],{"className":22655,"style":3866},[1844,1845],[1099,22657,22658],{},"传递法",[1788,22660,22662,22691],{"className":22661},[1791],[1788,22663,22665],{"className":22664},[1795],[1797,22666,22667],{"xmlns":1799},[1801,22668,22669,22688],{},[1804,22670,22671,22673,22675,22678,22680,22682,22684,22686],{},[1807,22672,2290],{},[1811,22674,6081],{},[1807,22676,22677],{"mathvariant":1982},"Λ",[1811,22679,2430],{"separator":1831},[1971,22681,1973],{},[1807,22683,22677],{"mathvariant":1982},[1811,22685,6081],{},[1807,22687,3841],{},[1823,22689,22690],{"encoding":1825},"A\\sim\\Lambda,\\ \\Lambda\\sim B",[1788,22692,22694,22712,22742],{"className":22693,"ariaHidden":1831},[1830],[1788,22695,22697,22700,22703,22706,22709],{"className":22696},[1835],[1788,22698],{"className":22699,"style":1840},[1839],[1788,22701,2290],{"className":22702},[1844,1845],[1788,22704],{"className":22705,"style":1851},[1850],[1788,22707,6081],{"className":22708},[1855],[1788,22710],{"className":22711,"style":1851},[1850],[1788,22713,22715,22718,22721,22724,22727,22730,22733,22736,22739],{"className":22714},[1835],[1788,22716],{"className":22717,"style":7685},[1839],[1788,22719,22677],{"className":22720},[1844],[1788,22722,2430],{"className":22723},[2474],[1788,22725,1973],{"className":22726},[1850],[1788,22728],{"className":22729,"style":2478},[1850],[1788,22731,22677],{"className":22732},[1844],[1788,22734],{"className":22735,"style":1851},[1850],[1788,22737,6081],{"className":22738},[1855],[1788,22740],{"className":22741,"style":1851},[1850],[1788,22743,22745,22748],{"className":22744},[1835],[1788,22746],{"className":22747,"style":1840},[1839],[1788,22749,3841],{"className":22750,"style":3866},[1844,1845],[1788,22752,22754,22771],{"className":22753},[1791],[1788,22755,22757],{"className":22756},[1795],[1797,22758,22759],{"xmlns":1799},[1801,22760,22761,22769],{},[1804,22762,22763,22765,22767],{},[1807,22764,2290],{},[1811,22766,6081],{},[1807,22768,3841],{},[1823,22770,21517],{"encoding":1825},[1788,22772,22774,22792],{"className":22773,"ariaHidden":1831},[1830],[1788,22775,22777,22780,22783,22786,22789],{"className":22776},[1835],[1788,22778],{"className":22779,"style":1840},[1839],[1788,22781,2290],{"className":22782},[1844,1845],[1788,22784],{"className":22785,"style":1851},[1850],[1788,22787,6081],{"className":22788},[1855],[1788,22790],{"className":22791,"style":1851},[1850],[1788,22793,22795,22798],{"className":22794},[1835],[1788,22796],{"className":22797,"style":1840},[1839],[1788,22799,3841],{"className":22800,"style":3866},[1844,1845],"，其中 ",[1788,22803,22805,22819],{"className":22804},[1791],[1788,22806,22808],{"className":22807},[1795],[1797,22809,22810],{"xmlns":1799},[1801,22811,22812,22816],{},[1804,22813,22814],{},[1807,22815,22677],{"mathvariant":1982},[1823,22817,22818],{"encoding":1825},"\\Lambda",[1788,22820,22822],{"className":22821,"ariaHidden":1831},[1830],[1788,22823,22825,22828],{"className":22824},[1835],[1788,22826],{"className":22827,"style":1840},[1839],[1788,22829,22677],{"className":22830},[1844]," 为对角阵。这就要说到矩阵的相似对角化。",[1096,22833,22834],{},[1099,22835,22836],{},"矩阵可相似对角化的条件：",[1912,22838,22839,22843,23161,23166],{},[1096,22840,22841],{},[1099,22842,14295],{},[1096,22844,6300,22845,20482,22873,22901,22902,11504,22933,8271,22961,22989,22990,20482,23018,22901,23046,11504,23074,23102,23103,23131,23132,23160],{},[1788,22846,22848,22861],{"className":22847},[1791],[1788,22849,22851],{"className":22850},[1795],[1797,22852,22853],{"xmlns":1799},[1801,22854,22855,22859],{},[1804,22856,22857],{},[1807,22858,2301],{},[1823,22860,2301],{"encoding":1825},[1788,22862,22864],{"className":22863,"ariaHidden":1831},[1830],[1788,22865,22867,22870],{"className":22866},[1835],[1788,22868],{"className":22869,"style":3114},[1839],[1788,22871,2301],{"className":22872},[1844,1845],[1788,22874,22876,22889],{"className":22875},[1791],[1788,22877,22879],{"className":22878},[1795],[1797,22880,22881],{"xmlns":1799},[1801,22882,22883,22887],{},[1804,22884,22885],{},[1807,22886,2290],{},[1823,22888,2290],{"encoding":1825},[1788,22890,22892],{"className":22891,"ariaHidden":1831},[1830],[1788,22893,22895,22898],{"className":22894},[1835],[1788,22896],{"className":22897,"style":1840},[1839],[1788,22899,2290],{"className":22900},[1844,1845]," 可相似对角化 ",[1788,22903,22905,22920],{"className":22904},[1791],[1788,22906,22908],{"className":22907},[1795],[1797,22909,22910],{"xmlns":1799},[1801,22911,22912,22917],{},[1804,22913,22914],{},[1811,22915,22916],{},"⟺",[1823,22918,22919],{"encoding":1825},"\\Longleftrightarrow",[1788,22921,22923],{"className":22922,"ariaHidden":1831},[1830],[1788,22924,22926,22930],{"className":22925},[1835],[1788,22927],{"className":22928,"style":22929},[1839],"height:0.549em;vertical-align:-0.024em;",[1788,22931,22916],{"className":22932},[1855],[1788,22934,22936,22949],{"className":22935},[1791],[1788,22937,22939],{"className":22938},[1795],[1797,22940,22941],{"xmlns":1799},[1801,22942,22943,22947],{},[1804,22944,22945],{},[1807,22946,2290],{},[1823,22948,2290],{"encoding":1825},[1788,22950,22952],{"className":22951,"ariaHidden":1831},[1830],[1788,22953,22955,22958],{"className":22954},[1835],[1788,22956],{"className":22957,"style":1840},[1839],[1788,22959,2290],{"className":22960},[1844,1845],[1788,22962,22964,22977],{"className":22963},[1791],[1788,22965,22967],{"className":22966},[1795],[1797,22968,22969],{"xmlns":1799},[1801,22970,22971,22975],{},[1804,22972,22973],{},[1807,22974,2301],{},[1823,22976,2301],{"encoding":1825},[1788,22978,22980],{"className":22979,"ariaHidden":1831},[1830],[1788,22981,22983,22986],{"className":22982},[1835],[1788,22984],{"className":22985,"style":3114},[1839],[1788,22987,2301],{"className":22988},[1844,1845]," 个线性无关的特征向量。\n② ",[1788,22991,22993,23006],{"className":22992},[1791],[1788,22994,22996],{"className":22995},[1795],[1797,22997,22998],{"xmlns":1799},[1801,22999,23000,23004],{},[1804,23001,23002],{},[1807,23003,2301],{},[1823,23005,2301],{"encoding":1825},[1788,23007,23009],{"className":23008,"ariaHidden":1831},[1830],[1788,23010,23012,23015],{"className":23011},[1835],[1788,23013],{"className":23014,"style":3114},[1839],[1788,23016,2301],{"className":23017},[1844,1845],[1788,23019,23021,23034],{"className":23020},[1791],[1788,23022,23024],{"className":23023},[1795],[1797,23025,23026],{"xmlns":1799},[1801,23027,23028,23032],{},[1804,23029,23030],{},[1807,23031,2290],{},[1823,23033,2290],{"encoding":1825},[1788,23035,23037],{"className":23036,"ariaHidden":1831},[1830],[1788,23038,23040,23043],{"className":23039},[1835],[1788,23041],{"className":23042,"style":1840},[1839],[1788,23044,2290],{"className":23045},[1844,1845],[1788,23047,23049,23062],{"className":23048},[1791],[1788,23050,23052],{"className":23051},[1795],[1797,23053,23054],{"xmlns":1799},[1801,23055,23056,23060],{},[1804,23057,23058],{},[1811,23059,22916],{},[1823,23061,22919],{"encoding":1825},[1788,23063,23065],{"className":23064,"ariaHidden":1831},[1830],[1788,23066,23068,23071],{"className":23067},[1835],[1788,23069],{"className":23070,"style":22929},[1839],[1788,23072,22916],{"className":23073},[1855],[1788,23075,23077,23090],{"className":23076},[1791],[1788,23078,23080],{"className":23079},[1795],[1797,23081,23082],{"xmlns":1799},[1801,23083,23084,23088],{},[1804,23085,23086],{},[1807,23087,2290],{},[1823,23089,2290],{"encoding":1825},[1788,23091,23093],{"className":23092,"ariaHidden":1831},[1830],[1788,23094,23096,23099],{"className":23095},[1835],[1788,23097],{"className":23098,"style":1840},[1839],[1788,23100,2290],{"className":23101},[1844,1845]," 对应于每个 ",[1788,23104,23106,23119],{"className":23105},[1791],[1788,23107,23109],{"className":23108},[1795],[1797,23110,23111],{"xmlns":1799},[1801,23112,23113,23117],{},[1804,23114,23115],{},[1807,23116,1938],{},[1823,23118,1938],{"encoding":1825},[1788,23120,23122],{"className":23121,"ariaHidden":1831},[1830],[1788,23123,23125,23128],{"className":23124},[1835],[1788,23126],{"className":23127,"style":1950},[1839],[1788,23129,1938],{"className":23130,"style":1954},[1844,1845]," 重特征值都有 ",[1788,23133,23135,23148],{"className":23134},[1791],[1788,23136,23138],{"className":23137},[1795],[1797,23139,23140],{"xmlns":1799},[1801,23141,23142,23146],{},[1804,23143,23144],{},[1807,23145,1938],{},[1823,23147,1938],{"encoding":1825},[1788,23149,23151],{"className":23150,"ariaHidden":1831},[1830],[1788,23152,23154,23157],{"className":23153},[1835],[1788,23155],{"className":23156,"style":1950},[1839],[1788,23158,1938],{"className":23159,"style":1954},[1844,1845]," 个线性无关的特征向量。",[1096,23162,23163],{},[1099,23164,23165],{},"充分条件：",[1096,23167,6592,23168,20482,23196,8271,23224,23252,23253,11504,23282,23310,23311,23339,23340,11504,23343,11504,23371,23399],{},[1788,23169,23171,23184],{"className":23170},[1791],[1788,23172,23174],{"className":23173},[1795],[1797,23175,23176],{"xmlns":1799},[1801,23177,23178,23182],{},[1804,23179,23180],{},[1807,23181,2301],{},[1823,23183,2301],{"encoding":1825},[1788,23185,23187],{"className":23186,"ariaHidden":1831},[1830],[1788,23188,23190,23193],{"className":23189},[1835],[1788,23191],{"className":23192,"style":3114},[1839],[1788,23194,2301],{"className":23195},[1844,1845],[1788,23197,23199,23212],{"className":23198},[1791],[1788,23200,23202],{"className":23201},[1795],[1797,23203,23204],{"xmlns":1799},[1801,23205,23206,23210],{},[1804,23207,23208],{},[1807,23209,2290],{},[1823,23211,2290],{"encoding":1825},[1788,23213,23215],{"className":23214,"ariaHidden":1831},[1830],[1788,23216,23218,23221],{"className":23217},[1835],[1788,23219],{"className":23220,"style":1840},[1839],[1788,23222,2290],{"className":23223},[1844,1845],[1788,23225,23227,23240],{"className":23226},[1791],[1788,23228,23230],{"className":23229},[1795],[1797,23231,23232],{"xmlns":1799},[1801,23233,23234,23238],{},[1804,23235,23236],{},[1807,23237,2301],{},[1823,23239,2301],{"encoding":1825},[1788,23241,23243],{"className":23242,"ariaHidden":1831},[1830],[1788,23244,23246,23249],{"className":23245},[1835],[1788,23247],{"className":23248,"style":3114},[1839],[1788,23250,2301],{"className":23251},[1844,1845]," 个不同特征值 ",[1788,23254,23256,23270],{"className":23255},[1791],[1788,23257,23259],{"className":23258},[1795],[1797,23260,23261],{"xmlns":1799},[1801,23262,23263,23267],{},[1804,23264,23265],{},[1811,23266,15270],{},[1823,23268,23269],{"encoding":1825},"\\Longrightarrow",[1788,23271,23273],{"className":23272,"ariaHidden":1831},[1830],[1788,23274,23276,23279],{"className":23275},[1835],[1788,23277],{"className":23278,"style":22929},[1839],[1788,23280,15270],{"className":23281},[1855],[1788,23283,23285,23298],{"className":23284},[1791],[1788,23286,23288],{"className":23287},[1795],[1797,23289,23290],{"xmlns":1799},[1801,23291,23292,23296],{},[1804,23293,23294],{},[1807,23295,2290],{},[1823,23297,2290],{"encoding":1825},[1788,23299,23301],{"className":23300,"ariaHidden":1831},[1830],[1788,23302,23304,23307],{"className":23303},[1835],[1788,23305],{"className":23306,"style":1840},[1839],[1788,23308,2290],{"className":23309},[1844,1845]," 可相似对角化。\n④ ",[1788,23312,23314,23327],{"className":23313},[1791],[1788,23315,23317],{"className":23316},[1795],[1797,23318,23319],{"xmlns":1799},[1801,23320,23321,23325],{},[1804,23322,23323],{},[1807,23324,2301],{},[1823,23326,2301],{"encoding":1825},[1788,23328,23330],{"className":23329,"ariaHidden":1831},[1830],[1788,23331,23333,23336],{"className":23332},[1835],[1788,23334],{"className":23335,"style":3114},[1839],[1788,23337,2301],{"className":23338},[1844,1845]," 阶矩阵为",[1099,23341,23342],{},"实对称矩阵",[1788,23344,23346,23359],{"className":23345},[1791],[1788,23347,23349],{"className":23348},[1795],[1797,23350,23351],{"xmlns":1799},[1801,23352,23353,23357],{},[1804,23354,23355],{},[1811,23356,15270],{},[1823,23358,23269],{"encoding":1825},[1788,23360,23362],{"className":23361,"ariaHidden":1831},[1830],[1788,23363,23365,23368],{"className":23364},[1835],[1788,23366],{"className":23367,"style":22929},[1839],[1788,23369,15270],{"className":23370},[1855],[1788,23372,23374,23387],{"className":23373},[1791],[1788,23375,23377],{"className":23376},[1795],[1797,23378,23379],{"xmlns":1799},[1801,23380,23381,23385],{},[1804,23382,23383],{},[1807,23384,2290],{},[1823,23386,2290],{"encoding":1825},[1788,23388,23390],{"className":23389,"ariaHidden":1831},[1830],[1788,23391,23393,23396],{"className":23392},[1835],[1788,23394],{"className":23395,"style":1840},[1839],[1788,23397,2290],{"className":23398},[1844,1845]," 可相似对角化。",[1096,23401,23402],{},"对于矩阵相似对角化的步骤：",[1912,23404,23405],{},[1096,23406,23407,23408,23661,23662,2080,23947,23975,23976,2389],{},"① 求特征值；\n② 求特征向量；\n③ 正交化（如果需要的话）、单位化 ",[1788,23409,23411,23459],{"className":23410},[1791],[1788,23412,23414],{"className":23413},[1795],[1797,23415,23416],{"xmlns":1799},[1801,23417,23418,23456],{},[1804,23419,23420,23426,23428,23434,23436,23442,23444,23446,23448,23450],{},[2881,23421,23422,23424],{},[1807,23423,16982],{},[1985,23425,2906],{},[1811,23427,2430],{"separator":1831},[2881,23429,23430,23432],{},[1807,23431,16982],{},[1985,23433,2896],{},[1811,23435,2430],{"separator":1831},[2881,23437,23438,23440],{},[1807,23439,16982],{},[1985,23441,2887],{},[1811,23443,2430],{"separator":1831},[1811,23445,9241],{},[1971,23447,2433],{},[1811,23449,2430],{"separator":1831},[2881,23451,23452,23454],{},[1807,23453,16982],{},[1807,23455,2301],{},[1823,23457,23458],{"encoding":1825},"\\eta_1,\\eta_2,\\eta_3,\\cdots,\\eta_n",[1788,23460,23462],{"className":23461,"ariaHidden":1831},[1830],[1788,23463,23465,23468,23508,23511,23514,23554,23557,23560,23600,23603,23606,23609,23612,23615,23618,23621],{"className":23464},[1835],[1788,23466],{"className":23467,"style":5356},[1839],[1788,23469,23471,23474],{"className":23470},[1844],[1788,23472,16982],{"className":23473,"style":17019},[1844,1845],[1788,23475,23477],{"className":23476},[1875],[1788,23478,23480,23500],{"className":23479},[1879,2931],[1788,23481,23483,23497],{"className":23482},[1883],[1788,23484,23486],{"className":23485,"style":2938},[1887],[1788,23487,23488,23491],{"style":17034},[1788,23489],{"className":23490,"style":1895},[1894],[1788,23492,23494],{"className":23493},[1899,1900,1901,1902],[1788,23495,2906],{"className":23496},[1844,1902],[1788,23498,2958],{"className":23499},[2957],[1788,23501,23503],{"className":23502},[1883],[1788,23504,23506],{"className":23505,"style":2965},[1887],[1788,23507],{},[1788,23509,2430],{"className":23510},[2474],[1788,23512],{"className":23513,"style":2478},[1850],[1788,23515,23517,23520],{"className":23516},[1844],[1788,23518,16982],{"className":23519,"style":17019},[1844,1845],[1788,23521,23523],{"className":23522},[1875],[1788,23524,23526,23546],{"className":23525},[1879,2931],[1788,23527,23529,23543],{"className":23528},[1883],[1788,23530,23532],{"className":23531,"style":2938},[1887],[1788,23533,23534,23537],{"style":17034},[1788,23535],{"className":23536,"style":1895},[1894],[1788,23538,23540],{"className":23539},[1899,1900,1901,1902],[1788,23541,2896],{"className":23542},[1844,1902],[1788,23544,2958],{"className":23545},[2957],[1788,23547,23549],{"className":23548},[1883],[1788,23550,23552],{"className":23551,"style":2965},[1887],[1788,23553],{},[1788,23555,2430],{"className":23556},[2474],[1788,23558],{"className":23559,"style":2478},[1850],[1788,23561,23563,23566],{"className":23562},[1844],[1788,23564,16982],{"className":23565,"style":17019},[1844,1845],[1788,23567,23569],{"className":23568},[1875],[1788,23570,23572,23592],{"className":23571},[1879,2931],[1788,23573,23575,23589],{"className":23574},[1883],[1788,23576,23578],{"className":23577,"style":2938},[1887],[1788,23579,23580,23583],{"style":17034},[1788,23581],{"className":23582,"style":1895},[1894],[1788,23584,23586],{"className":23585},[1899,1900,1901,1902],[1788,23587,2887],{"className":23588},[1844,1902],[1788,23590,2958],{"className":23591},[2957],[1788,23593,23595],{"className":23594},[1883],[1788,23596,23598],{"className":23597,"style":2965},[1887],[1788,23599],{},[1788,23601,2430],{"className":23602},[2474],[1788,23604],{"className":23605,"style":2478},[1850],[1788,23607,9241],{"className":23608},[9480],[1788,23610],{"className":23611,"style":2478},[1850],[1788,23613],{"className":23614,"style":2478},[1850],[1788,23616,2430],{"className":23617},[2474],[1788,23619],{"className":23620,"style":2478},[1850],[1788,23622,23624,23627],{"className":23623},[1844],[1788,23625,16982],{"className":23626,"style":17019},[1844,1845],[1788,23628,23630],{"className":23629},[1875],[1788,23631,23633,23653],{"className":23632},[1879,2931],[1788,23634,23636,23650],{"className":23635},[1883],[1788,23637,23639],{"className":23638,"style":17879},[1887],[1788,23640,23641,23644],{"style":17034},[1788,23642],{"className":23643,"style":1895},[1894],[1788,23645,23647],{"className":23646},[1899,1900,1901,1902],[1788,23648,2301],{"className":23649},[1844,1845,1902],[1788,23651,2958],{"className":23652},[2957],[1788,23654,23656],{"className":23655},[1883],[1788,23657,23659],{"className":23658,"style":2965},[1887],[1788,23660],{},"；\n④ 令 ",[1788,23663,23665,23721],{"className":23664},[1791],[1788,23666,23668],{"className":23667},[1795],[1797,23669,23670],{"xmlns":1799},[1801,23671,23672,23718],{},[1804,23673,23674,23676,23678,23680,23686,23688,23694,23696,23702,23704,23706,23708,23710,23716],{},[1807,23675,7672],{},[1811,23677,1813],{},[1811,23679,14861],{"stretchy":1976},[2881,23681,23682,23684],{},[1807,23683,16982],{},[1985,23685,2906],{},[1811,23687,2430],{"separator":1831},[2881,23689,23690,23692],{},[1807,23691,16982],{},[1985,23693,2896],{},[1811,23695,2430],{"separator":1831},[2881,23697,23698,23700],{},[1807,23699,16982],{},[1985,23701,2887],{},[1811,23703,2430],{"separator":1831},[1811,23705,9241],{},[1971,23707,2433],{},[1811,23709,2430],{"separator":1831},[2881,23711,23712,23714],{},[1807,23713,16982],{},[1807,23715,2301],{},[1811,23717,14871],{"stretchy":1976},[1823,23719,23720],{"encoding":1825},"Q=[\\eta_1,\\eta_2,\\eta_3,\\cdots,\\eta_n]",[1788,23722,23724,23742],{"className":23723,"ariaHidden":1831},[1830],[1788,23725,23727,23730,23733,23736,23739],{"className":23726},[1835],[1788,23728],{"className":23729,"style":7685},[1839],[1788,23731,7672],{"className":23732},[1844,1845],[1788,23734],{"className":23735,"style":1851},[1850],[1788,23737,1813],{"className":23738},[1855],[1788,23740],{"className":23741,"style":1851},[1850],[1788,23743,23745,23748,23751,23791,23794,23797,23837,23840,23843,23883,23886,23889,23892,23895,23898,23901,23904,23944],{"className":23744},[1835],[1788,23746],{"className":23747,"style":2003},[1839],[1788,23749,14861],{"className":23750},[2013],[1788,23752,23754,23757],{"className":23753},[1844],[1788,23755,16982],{"className":23756,"style":17019},[1844,1845],[1788,23758,23760],{"className":23759},[1875],[1788,23761,23763,23783],{"className":23762},[1879,2931],[1788,23764,23766,23780],{"className":23765},[1883],[1788,23767,23769],{"className":23768,"style":2938},[1887],[1788,23770,23771,23774],{"style":17034},[1788,23772],{"className":23773,"style":1895},[1894],[1788,23775,23777],{"className":23776},[1899,1900,1901,1902],[1788,23778,2906],{"className":23779},[1844,1902],[1788,23781,2958],{"className":23782},[2957],[1788,23784,23786],{"className":23785},[1883],[1788,23787,23789],{"className":23788,"style":2965},[1887],[1788,23790],{},[1788,23792,2430],{"className":23793},[2474],[1788,23795],{"className":23796,"style":2478},[1850],[1788,23798,23800,23803],{"className":23799},[1844],[1788,23801,16982],{"className":23802,"style":17019},[1844,1845],[1788,23804,23806],{"className":23805},[1875],[1788,23807,23809,23829],{"className":23808},[1879,2931],[1788,23810,23812,23826],{"className":23811},[1883],[1788,23813,23815],{"className":23814,"style":2938},[1887],[1788,23816,23817,23820],{"style":17034},[1788,23818],{"className":23819,"style":1895},[1894],[1788,23821,23823],{"className":23822},[1899,1900,1901,1902],[1788,23824,2896],{"className":23825},[1844,1902],[1788,23827,2958],{"className":23828},[2957],[1788,23830,23832],{"className":23831},[1883],[1788,23833,23835],{"className":23834,"style":2965},[1887],[1788,23836],{},[1788,23838,2430],{"className":23839},[2474],[1788,23841],{"className":23842,"style":2478},[1850],[1788,23844,23846,23849],{"className":23845},[1844],[1788,23847,16982],{"className":23848,"style":17019},[1844,1845],[1788,23850,23852],{"className":23851},[1875],[1788,23853,23855,23875],{"className":23854},[1879,2931],[1788,23856,23858,23872],{"className":23857},[1883],[1788,23859,23861],{"className":23860,"style":2938},[1887],[1788,23862,23863,23866],{"style":17034},[1788,23864],{"className":23865,"style":1895},[1894],[1788,23867,23869],{"className":23868},[1899,1900,1901,1902],[1788,23870,2887],{"className":23871},[1844,1902],[1788,23873,2958],{"className":23874},[2957],[1788,23876,23878],{"className":23877},[1883],[1788,23879,23881],{"className":23880,"style":2965},[1887],[1788,23882],{},[1788,23884,2430],{"className":23885},[2474],[1788,23887],{"className":23888,"style":2478},[1850],[1788,23890,9241],{"className":23891},[9480],[1788,23893],{"className":23894,"style":2478},[1850],[1788,23896],{"className":23897,"style":2478},[1850],[1788,23899,2430],{"className":23900},[2474],[1788,23902],{"className":23903,"style":2478},[1850],[1788,23905,23907,23910],{"className":23906},[1844],[1788,23908,16982],{"className":23909,"style":17019},[1844,1845],[1788,23911,23913],{"className":23912},[1875],[1788,23914,23916,23936],{"className":23915},[1879,2931],[1788,23917,23919,23933],{"className":23918},[1883],[1788,23920,23922],{"className":23921,"style":17879},[1887],[1788,23923,23924,23927],{"style":17034},[1788,23925],{"className":23926,"style":1895},[1894],[1788,23928,23930],{"className":23929},[1899,1900,1901,1902],[1788,23931,2301],{"className":23932},[1844,1845,1902],[1788,23934,2958],{"className":23935},[2957],[1788,23937,23939],{"className":23938},[1883],[1788,23940,23942],{"className":23941,"style":2965},[1887],[1788,23943],{},[1788,23945,14871],{"className":23946},[2079],[1788,23948,23950,23963],{"className":23949},[1791],[1788,23951,23953],{"className":23952},[1795],[1797,23954,23955],{"xmlns":1799},[1801,23956,23957,23961],{},[1804,23958,23959],{},[1807,23960,7672],{},[1823,23962,7672],{"encoding":1825},[1788,23964,23966],{"className":23965,"ariaHidden":1831},[1830],[1788,23967,23969,23972],{"className":23968},[1835],[1788,23970],{"className":23971,"style":7685},[1839],[1788,23973,7672],{"className":23974},[1844,1845]," 为正交矩阵，且 ",[1788,23977,23979,24021],{"className":23978},[1791],[1788,23980,23982],{"className":23981},[1795],[1797,23983,23984],{"xmlns":1799},[1801,23985,23986,24018],{},[1804,23987,23988,23998,24000,24002,24004,24010,24012,24014,24016],{},[1815,23989,23990,23992],{},[1807,23991,7672],{},[1804,23993,23994,23996],{},[1811,23995,3250],{},[1985,23997,2906],{},[1807,23999,2290],{},[1807,24001,7672],{},[1811,24003,1813],{},[1815,24005,24006,24008],{},[1807,24007,7672],{},[1807,24009,1821],{},[1807,24011,2290],{},[1807,24013,7672],{},[1811,24015,1813],{},[1807,24017,22677],{"mathvariant":1982},[1823,24019,24020],{"encoding":1825},"Q^{-1}AQ=Q^{T}AQ=\\Lambda",[1788,24022,24024,24081,24134],{"className":24023,"ariaHidden":1831},[1830],[1788,24025,24027,24031,24066,24069,24072,24075,24078],{"className":24026},[1835],[1788,24028],{"className":24029,"style":24030},[1839],"height:1.0085em;vertical-align:-0.1944em;",[1788,24032,24034,24037],{"className":24033},[1844],[1788,24035,7672],{"className":24036},[1844,1845],[1788,24038,24040],{"className":24039},[1875],[1788,24041,24043],{"className":24042},[1879],[1788,24044,24046],{"className":24045},[1883],[1788,24047,24049],{"className":24048,"style":3265},[1887],[1788,24050,24051,24054],{"style":1890},[1788,24052],{"className":24053,"style":1895},[1894],[1788,24055,24057],{"className":24056},[1899,1900,1901,1902],[1788,24058,24060,24063],{"className":24059},[1844,1902],[1788,24061,3250],{"className":24062},[1844,1902],[1788,24064,2906],{"className":24065},[1844,1902],[1788,24067,2290],{"className":24068},[1844,1845],[1788,24070,7672],{"className":24071},[1844,1845],[1788,24073],{"className":24074,"style":1851},[1850],[1788,24076,1813],{"className":24077},[1855],[1788,24079],{"className":24080,"style":1851},[1850],[1788,24082,24084,24087,24119,24122,24125,24128,24131],{"className":24083},[1835],[1788,24085],{"className":24086,"style":20537},[1839],[1788,24088,24090,24093],{"className":24089},[1844],[1788,24091,7672],{"className":24092},[1844,1845],[1788,24094,24096],{"className":24095},[1875],[1788,24097,24099],{"className":24098},[1879],[1788,24100,24102],{"className":24101},[1883],[1788,24103,24105],{"className":24104,"style":1865},[1887],[1788,24106,24107,24110],{"style":1890},[1788,24108],{"className":24109,"style":1895},[1894],[1788,24111,24113],{"className":24112},[1899,1900,1901,1902],[1788,24114,24116],{"className":24115},[1844,1902],[1788,24117,1821],{"className":24118,"style":1909},[1844,1845,1902],[1788,24120,2290],{"className":24121},[1844,1845],[1788,24123,7672],{"className":24124},[1844,1845],[1788,24126],{"className":24127,"style":1851},[1850],[1788,24129,1813],{"className":24130},[1855],[1788,24132],{"className":24133,"style":1851},[1850],[1788,24135,24137,24140],{"className":24136},[1835],[1788,24138],{"className":24139,"style":1840},[1839],[1788,24141,22677],{"className":24142},[1844],[1096,24144,24145,24146,24174,24175,24259],{},"上面提到了实对称矩阵，实对称矩阵就是组成 ",[1788,24147,24149,24162],{"className":24148},[1791],[1788,24150,24152],{"className":24151},[1795],[1797,24153,24154],{"xmlns":1799},[1801,24155,24156,24160],{},[1804,24157,24158],{},[1807,24159,2290],{},[1823,24161,2290],{"encoding":1825},[1788,24163,24165],{"className":24164,"ariaHidden":1831},[1830],[1788,24166,24168,24171],{"className":24167},[1835],[1788,24169],{"className":24170,"style":1840},[1839],[1788,24172,2290],{"className":24173},[1844,1845]," 的元素都是实数（即 ",[1788,24176,24178,24200],{"className":24177},[1791],[1788,24179,24181],{"className":24180},[1795],[1797,24182,24183],{"xmlns":1799},[1801,24184,24185,24197],{},[1804,24186,24187,24193,24195],{},[1815,24188,24189,24191],{},[1807,24190,2290],{},[1807,24192,1821],{},[1811,24194,1813],{},[1807,24196,2290],{},[1823,24198,24199],{"encoding":1825},"A^{T}=A",[1788,24201,24203,24250],{"className":24202,"ariaHidden":1831},[1830],[1788,24204,24206,24209,24241,24244,24247],{"className":24205},[1835],[1788,24207],{"className":24208,"style":1865},[1839],[1788,24210,24212,24215],{"className":24211},[1844],[1788,24213,2290],{"className":24214},[1844,1845],[1788,24216,24218],{"className":24217},[1875],[1788,24219,24221],{"className":24220},[1879],[1788,24222,24224],{"className":24223},[1883],[1788,24225,24227],{"className":24226,"style":1865},[1887],[1788,24228,24229,24232],{"style":1890},[1788,24230],{"className":24231,"style":1895},[1894],[1788,24233,24235],{"className":24234},[1899,1900,1901,1902],[1788,24236,24238],{"className":24237},[1844,1902],[1788,24239,1821],{"className":24240,"style":1909},[1844,1845,1902],[1788,24242],{"className":24243,"style":1851},[1850],[1788,24245,1813],{"className":24246},[1855],[1788,24248],{"className":24249,"style":1851},[1850],[1788,24251,24253,24256],{"className":24252},[1835],[1788,24254],{"className":24255,"style":1840},[1839],[1788,24257,2290],{"className":24258},[1844,1845],"）。对于实对称矩阵要记住：",[1096,24261,24262],{},[2114,24263],{"alt":23342,"src":24264},"https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2250f42.png",[1912,24266,24267,24272],{},[1096,24268,24269],{},[1099,24270,24271],{},"对于正交，你需要记住：",[1096,24273,6300,24274,2080,24363,24404,24405,2080,24494,24522,24523,2389],{},[1788,24275,24277,24301],{"className":24276},[1791],[1788,24278,24280],{"className":24279},[1795],[1797,24281,24282],{"xmlns":1799},[1801,24283,24284,24298],{},[1804,24285,24286,24292,24294,24296],{},[1815,24287,24288,24290],{},[1807,24289,3101],{},[1807,24291,1821],{},[1807,24293,2850],{},[1811,24295,1813],{},[1985,24297,1987],{},[1823,24299,24300],{"encoding":1825},"\\alpha^{T}\\beta=0",[1788,24302,24304,24354],{"className":24303,"ariaHidden":1831},[1830],[1788,24305,24307,24310,24342,24345,24348,24351],{"className":24306},[1835],[1788,24308],{"className":24309,"style":20537},[1839],[1788,24311,24313,24316],{"className":24312},[1844],[1788,24314,3101],{"className":24315,"style":3118},[1844,1845],[1788,24317,24319],{"className":24318},[1875],[1788,24320,24322],{"className":24321},[1879],[1788,24323,24325],{"className":24324},[1883],[1788,24326,24328],{"className":24327,"style":1865},[1887],[1788,24329,24330,24333],{"style":1890},[1788,24331],{"className":24332,"style":1895},[1894],[1788,24334,24336],{"className":24335},[1899,1900,1901,1902],[1788,24337,24339],{"className":24338},[1844,1902],[1788,24340,1821],{"className":24341,"style":1909},[1844,1845,1902],[1788,24343,2850],{"className":24344,"style":2866},[1844,1845],[1788,24346],{"className":24347,"style":1851},[1850],[1788,24349,1813],{"className":24350},[1855],[1788,24352],{"className":24353,"style":1851},[1850],[1788,24355,24357,24360],{"className":24356},[1835],[1788,24358],{"className":24359,"style":4209},[1839],[1788,24361,1987],{"className":24362},[1844],[1788,24364,24366,24383],{"className":24365},[1791],[1788,24367,24369],{"className":24368},[1795],[1797,24370,24371],{"xmlns":1799},[1801,24372,24373,24381],{},[1804,24374,24375,24377,24379],{},[1807,24376,3101],{},[1811,24378,2430],{"separator":1831},[1807,24380,2850],{},[1823,24382,20594],{"encoding":1825},[1788,24384,24386],{"className":24385,"ariaHidden":1831},[1830],[1788,24387,24389,24392,24395,24398,24401],{"className":24388},[1835],[1788,24390],{"className":24391,"style":2041},[1839],[1788,24393,3101],{"className":24394,"style":3118},[1844,1845],[1788,24396,2430],{"className":24397},[2474],[1788,24399],{"className":24400,"style":2478},[1850],[1788,24402,2850],{"className":24403,"style":2866},[1844,1845]," 是正交向量。\n② 若满足 ",[1788,24406,24408,24432],{"className":24407},[1791],[1788,24409,24411],{"className":24410},[1795],[1797,24412,24413],{"xmlns":1799},[1801,24414,24415,24429],{},[1804,24416,24417,24423,24425,24427],{},[1815,24418,24419,24421],{},[1807,24420,2290],{},[1807,24422,1821],{},[1807,24424,2290],{},[1811,24426,1813],{},[1807,24428,3192],{},[1823,24430,24431],{"encoding":1825},"A^{T}A=E",[1788,24433,24435,24485],{"className":24434,"ariaHidden":1831},[1830],[1788,24436,24438,24441,24473,24476,24479,24482],{"className":24437},[1835],[1788,24439],{"className":24440,"style":1865},[1839],[1788,24442,24444,24447],{"className":24443},[1844],[1788,24445,2290],{"className":24446},[1844,1845],[1788,24448,24450],{"className":24449},[1875],[1788,24451,24453],{"className":24452},[1879],[1788,24454,24456],{"className":24455},[1883],[1788,24457,24459],{"className":24458,"style":1865},[1887],[1788,24460,24461,24464],{"style":1890},[1788,24462],{"className":24463,"style":1895},[1894],[1788,24465,24467],{"className":24466},[1899,1900,1901,1902],[1788,24468,24470],{"className":24469},[1844,1902],[1788,24471,1821],{"className":24472,"style":1909},[1844,1845,1902],[1788,24474,2290],{"className":24475},[1844,1845],[1788,24477],{"className":24478,"style":1851},[1850],[1788,24480,1813],{"className":24481},[1855],[1788,24483],{"className":24484,"style":1851},[1850],[1788,24486,24488,24491],{"className":24487},[1835],[1788,24489],{"className":24490,"style":1840},[1839],[1788,24492,3192],{"className":24493,"style":3222},[1844,1845],[1788,24495,24497,24510],{"className":24496},[1791],[1788,24498,24500],{"className":24499},[1795],[1797,24501,24502],{"xmlns":1799},[1801,24503,24504,24508],{},[1804,24505,24506],{},[1807,24507,2290],{},[1823,24509,2290],{"encoding":1825},[1788,24511,24513],{"className":24512,"ariaHidden":1831},[1830],[1788,24514,24516,24519],{"className":24515},[1835],[1788,24517],{"className":24518,"style":1840},[1839],[1788,24520,2290],{"className":24521},[1844,1845]," 是正交矩阵。\n③ ",[1788,24524,24526,24570],{"className":24525},[1791],[1788,24527,24529],{"className":24528},[1795],[1797,24530,24531],{"xmlns":1799},[1801,24532,24533,24567],{},[1804,24534,24535,24541,24543,24545,24547,24549,24559,24561],{},[1815,24536,24537,24539],{},[1807,24538,2290],{},[1807,24540,1821],{},[1807,24542,2290],{},[1811,24544,1813],{},[1807,24546,3192],{},[1811,24548,22916],{},[1815,24550,24551,24553],{},[1807,24552,2290],{},[1804,24554,24555,24557],{},[1811,24556,3250],{},[1985,24558,2906],{},[1811,24560,1813],{},[1815,24562,24563,24565],{},[1807,24564,2290],{},[1807,24566,1821],{},[1823,24568,24569],{"encoding":1825},"A^{T}A=E\\Longleftrightarrow A^{-1}=A^{T}",[1788,24571,24573,24623,24642,24692],{"className":24572,"ariaHidden":1831},[1830],[1788,24574,24576,24579,24611,24614,24617,24620],{"className":24575},[1835],[1788,24577],{"className":24578,"style":1865},[1839],[1788,24580,24582,24585],{"className":24581},[1844],[1788,24583,2290],{"className":24584},[1844,1845],[1788,24586,24588],{"className":24587},[1875],[1788,24589,24591],{"className":24590},[1879],[1788,24592,24594],{"className":24593},[1883],[1788,24595,24597],{"className":24596,"style":1865},[1887],[1788,24598,24599,24602],{"style":1890},[1788,24600],{"className":24601,"style":1895},[1894],[1788,24603,24605],{"className":24604},[1899,1900,1901,1902],[1788,24606,24608],{"className":24607},[1844,1902],[1788,24609,1821],{"className":24610,"style":1909},[1844,1845,1902],[1788,24612,2290],{"className":24613},[1844,1845],[1788,24615],{"className":24616,"style":1851},[1850],[1788,24618,1813],{"className":24619},[1855],[1788,24621],{"className":24622,"style":1851},[1850],[1788,24624,24626,24630,24633,24636,24639],{"className":24625},[1835],[1788,24627],{"className":24628,"style":24629},[1839],"height:0.7073em;vertical-align:-0.024em;",[1788,24631,3192],{"className":24632,"style":3222},[1844,1845],[1788,24634],{"className":24635,"style":1851},[1850],[1788,24637,22916],{"className":24638},[1855],[1788,24640],{"className":24641,"style":1851},[1850],[1788,24643,24645,24648,24683,24686,24689],{"className":24644},[1835],[1788,24646],{"className":24647,"style":3265},[1839],[1788,24649,24651,24654],{"className":24650},[1844],[1788,24652,2290],{"className":24653},[1844,1845],[1788,24655,24657],{"className":24656},[1875],[1788,24658,24660],{"className":24659},[1879],[1788,24661,24663],{"className":24662},[1883],[1788,24664,24666],{"className":24665,"style":3265},[1887],[1788,24667,24668,24671],{"style":1890},[1788,24669],{"className":24670,"style":1895},[1894],[1788,24672,24674],{"className":24673},[1899,1900,1901,1902],[1788,24675,24677,24680],{"className":24676},[1844,1902],[1788,24678,3250],{"className":24679},[1844,1902],[1788,24681,2906],{"className":24682},[1844,1902],[1788,24684],{"className":24685,"style":1851},[1850],[1788,24687,1813],{"className":24688},[1855],[1788,24690],{"className":24691,"style":1851},[1850],[1788,24693,24695,24698],{"className":24694},[1835],[1788,24696],{"className":24697,"style":1865},[1839],[1788,24699,24701,24704],{"className":24700},[1844],[1788,24702,2290],{"className":24703},[1844,1845],[1788,24705,24707],{"className":24706},[1875],[1788,24708,24710],{"className":24709},[1879],[1788,24711,24713],{"className":24712},[1883],[1788,24714,24716],{"className":24715,"style":1865},[1887],[1788,24717,24718,24721],{"style":1890},[1788,24719],{"className":24720,"style":1895},[1894],[1788,24722,24724],{"className":24723},[1899,1900,1901,1902],[1788,24725,24727],{"className":24726},[1844,1902],[1788,24728,1821],{"className":24729,"style":1909},[1844,1845,1902],[1096,24731,11292],{},[1096,24733,24734],{},[2114,24735],{"alt":24736,"src":24737},"正交例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be20c78f6.png",[1096,24739,24740],{},[1099,24741,24742],{},"不可对角化的矩阵怎么判断相似：",[1096,24744,24745],{},[1099,24746,11292],{},[1096,24748,24749],{},[2114,24750],{"alt":24751,"src":24752},"不可对角化例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2286469.png",[1912,24754,24755,24814,25074],{},[1096,24756,16384,24757,8852,24785,24813],{},[1788,24758,24760,24773],{"className":24759},[1791],[1788,24761,24763],{"className":24762},[1795],[1797,24764,24765],{"xmlns":1799},[1801,24766,24767,24771],{},[1804,24768,24769],{},[1807,24770,2290],{},[1823,24772,2290],{"encoding":1825},[1788,24774,24776],{"className":24775,"ariaHidden":1831},[1830],[1788,24777,24779,24782],{"className":24778},[1835],[1788,24780],{"className":24781,"style":1840},[1839],[1788,24783,2290],{"className":24784},[1844,1845],[1788,24786,24788,24801],{"className":24787},[1791],[1788,24789,24791],{"className":24790},[1795],[1797,24792,24793],{"xmlns":1799},[1801,24794,24795,24799],{},[1804,24796,24797],{},[1807,24798,3841],{},[1823,24800,3841],{"encoding":1825},[1788,24802,24804],{"className":24803,"ariaHidden":1831},[1830],[1788,24805,24807,24810],{"className":24806},[1835],[1788,24808],{"className":24809,"style":1840},[1839],[1788,24811,3841],{"className":24812,"style":3866},[1844,1845]," 相似，那么：",[1096,24815,24816,24817,24845,24846,24874,24875,8852,24974,25073],{},"对于任意实数 ",[1788,24818,24820,24833],{"className":24819},[1791],[1788,24821,24823],{"className":24822},[1795],[1797,24824,24825],{"xmlns":1799},[1801,24826,24827,24831],{},[1804,24828,24829],{},[1807,24830,1938],{},[1823,24832,1938],{"encoding":1825},[1788,24834,24836],{"className":24835,"ariaHidden":1831},[1830],[1788,24837,24839,24842],{"className":24838},[1835],[1788,24840],{"className":24841,"style":1950},[1839],[1788,24843,1938],{"className":24844,"style":1954},[1844,1845]," 和整数 ",[1788,24847,24849,24862],{"className":24848},[1791],[1788,24850,24852],{"className":24851},[1795],[1797,24853,24854],{"xmlns":1799},[1801,24855,24856,24860],{},[1804,24857,24858],{},[1807,24859,2301],{},[1823,24861,2301],{"encoding":1825},[1788,24863,24865],{"className":24864,"ariaHidden":1831},[1830],[1788,24866,24868,24871],{"className":24867},[1835],[1788,24869],{"className":24870,"style":3114},[1839],[1788,24872,2301],{"className":24873},[1844,1845],"，有 ",[1788,24876,24878,24906],{"className":24877},[1791],[1788,24879,24881],{"className":24880},[1795],[1797,24882,24883],{"xmlns":1799},[1801,24884,24885,24903],{},[1804,24886,24887,24889,24891,24893,24895,24897],{},[1811,24888,1977],{"stretchy":1976},[1807,24890,2290],{},[1811,24892,2899],{},[1807,24894,1938],{},[1807,24896,3192],{},[1815,24898,24899,24901],{},[1811,24900,1990],{"stretchy":1976},[1807,24902,2301],{},[1823,24904,24905],{"encoding":1825},"(A+kE)^{n}",[1788,24907,24909,24930],{"className":24908,"ariaHidden":1831},[1830],[1788,24910,24912,24915,24918,24921,24924,24927],{"className":24911},[1835],[1788,24913],{"className":24914,"style":2003},[1839],[1788,24916,1977],{"className":24917},[2013],[1788,24919,2290],{"className":24920},[1844,1845],[1788,24922],{"className":24923,"style":3029},[1850],[1788,24925,2899],{"className":24926},[3033],[1788,24928],{"className":24929,"style":3029},[1850],[1788,24931,24933,24936,24939,24942],{"className":24932},[1835],[1788,24934],{"className":24935,"style":2003},[1839],[1788,24937,1938],{"className":24938,"style":1954},[1844,1845],[1788,24940,3192],{"className":24941,"style":3222},[1844,1845],[1788,24943,24945,24948],{"className":24944},[2079],[1788,24946,1990],{"className":24947},[2079],[1788,24949,24951],{"className":24950},[1875],[1788,24952,24954],{"className":24953},[1879],[1788,24955,24957],{"className":24956},[1883],[1788,24958,24960],{"className":24959,"style":2365},[1887],[1788,24961,24962,24965],{"style":1890},[1788,24963],{"className":24964,"style":1895},[1894],[1788,24966,24968],{"className":24967},[1899,1900,1901,1902],[1788,24969,24971],{"className":24970},[1844,1902],[1788,24972,2301],{"className":24973},[1844,1845,1902],[1788,24975,24977,25005],{"className":24976},[1791],[1788,24978,24980],{"className":24979},[1795],[1797,24981,24982],{"xmlns":1799},[1801,24983,24984,25002],{},[1804,24985,24986,24988,24990,24992,24994,24996],{},[1811,24987,1977],{"stretchy":1976},[1807,24989,3841],{},[1811,24991,2899],{},[1807,24993,1938],{},[1807,24995,3192],{},[1815,24997,24998,25000],{},[1811,24999,1990],{"stretchy":1976},[1807,25001,2301],{},[1823,25003,25004],{"encoding":1825},"(B+kE)^{n}",[1788,25006,25008,25029],{"className":25007,"ariaHidden":1831},[1830],[1788,25009,25011,25014,25017,25020,25023,25026],{"className":25010},[1835],[1788,25012],{"className":25013,"style":2003},[1839],[1788,25015,1977],{"className":25016},[2013],[1788,25018,3841],{"className":25019,"style":3866},[1844,1845],[1788,25021],{"className":25022,"style":3029},[1850],[1788,25024,2899],{"className":25025},[3033],[1788,25027],{"className":25028,"style":3029},[1850],[1788,25030,25032,25035,25038,25041],{"className":25031},[1835],[1788,25033],{"className":25034,"style":2003},[1839],[1788,25036,1938],{"className":25037,"style":1954},[1844,1845],[1788,25039,3192],{"className":25040,"style":3222},[1844,1845],[1788,25042,25044,25047],{"className":25043},[2079],[1788,25045,1990],{"className":25046},[2079],[1788,25048,25050],{"className":25049},[1875],[1788,25051,25053],{"className":25052},[1879],[1788,25054,25056],{"className":25055},[1883],[1788,25057,25059],{"className":25058,"style":2365},[1887],[1788,25060,25061,25064],{"style":1890},[1788,25062],{"className":25063,"style":1895},[1894],[1788,25065,25067],{"className":25066},[1899,1900,1901,1902],[1788,25068,25070],{"className":25069},[1844,1902],[1788,25071,2301],{"className":25072},[1844,1845,1902]," 相似。",[1096,25075,25076,25077,25174],{},"对于上面这道题，取 ",[1788,25078,25080,25110],{"className":25079},[1791],[1788,25081,25083],{"className":25082},[1795],[1797,25084,25085],{"xmlns":1799},[1801,25086,25087,25107],{},[1804,25088,25089,25091,25093,25095,25097,25099,25101,25103,25105],{},[1807,25090,1938],{},[1811,25092,1813],{},[1811,25094,3250],{},[1985,25096,2906],{},[1811,25098,2430],{"separator":1831},[1971,25100,1973],{},[1807,25102,2301],{},[1811,25104,1813],{},[1985,25106,2906],{},[1823,25108,25109],{"encoding":1825},"k=-1,\\ n=1",[1788,25111,25113,25131,25165],{"className":25112,"ariaHidden":1831},[1830],[1788,25114,25116,25119,25122,25125,25128],{"className":25115},[1835],[1788,25117],{"className":25118,"style":1950},[1839],[1788,25120,1938],{"className":25121,"style":1954},[1844,1845],[1788,25123],{"className":25124,"style":1851},[1850],[1788,25126,1813],{"className":25127},[1855],[1788,25129],{"className":25130,"style":1851},[1850],[1788,25132,25134,25138,25141,25144,25147,25150,25153,25156,25159,25162],{"className":25133},[1835],[1788,25135],{"className":25136,"style":25137},[1839],"height:0.8389em;vertical-align:-0.1944em;",[1788,25139,3250],{"className":25140},[1844],[1788,25142,2906],{"className":25143},[1844],[1788,25145,2430],{"className":25146},[2474],[1788,25148,1973],{"className":25149},[1850],[1788,25151],{"className":25152,"style":2478},[1850],[1788,25154,2301],{"className":25155},[1844,1845],[1788,25157],{"className":25158,"style":1851},[1850],[1788,25160,1813],{"className":25161},[1855],[1788,25163],{"className":25164,"style":1851},[1850],[1788,25166,25168,25171],{"className":25167},[1835],[1788,25169],{"className":25170,"style":4209},[1839],[1788,25172,2906],{"className":25173},[1844],"，判断哪两个矩阵相似。",[1096,25176,25177],{},[1099,25178,25179],{},"矩阵相似还可得出：",[1912,25181,25182],{},[1096,25183,6300,25184,25419,25420,9890,25470,25498,25499,25781,25782,2080,25832,20573,25949,25990,25991,2080,26041,2389],{},[1788,25185,25187,25244],{"className":25186},[1791],[1788,25188,25190],{"className":25189},[1795],[1797,25191,25192],{"xmlns":1799},[1801,25193,25194,25241],{},[1804,25195,25196,25198,25200,25202,25204,25210,25212,25218,25220,25222,25225,25227,25229,25231,25233,25235,25237,25239],{},[1807,25197,2290],{},[1811,25199,6081],{},[1807,25201,3841],{},[1811,25203,15270],{},[1815,25205,25206,25208],{},[1807,25207,2290],{},[1807,25209,1938],{},[1811,25211,6081],{},[1815,25213,25214,25216],{},[1807,25215,3841],{},[1807,25217,1938],{},[1811,25219,2430],{"separator":1831},[1971,25221,1973],{},[1807,25223,25224],{},"f",[1811,25226,1977],{"stretchy":1976},[1807,25228,2290],{},[1811,25230,1990],{"stretchy":1976},[1811,25232,6081],{},[1807,25234,25224],{},[1811,25236,1977],{"stretchy":1976},[1807,25238,3841],{},[1811,25240,1990],{"stretchy":1976},[1823,25242,25243],{"encoding":1825},"A\\sim B\\Longrightarrow A^{k}\\sim B^{k},\\ f(A)\\sim f(B)",[1788,25245,25247,25265,25283,25331,25401],{"className":25246,"ariaHidden":1831},[1830],[1788,25248,25250,25253,25256,25259,25262],{"className":25249},[1835],[1788,25251],{"className":25252,"style":1840},[1839],[1788,25254,2290],{"className":25255},[1844,1845],[1788,25257],{"className":25258,"style":1851},[1850],[1788,25260,6081],{"className":25261},[1855],[1788,25263],{"className":25264,"style":1851},[1850],[1788,25266,25268,25271,25274,25277,25280],{"className":25267},[1835],[1788,25269],{"className":25270,"style":24629},[1839],[1788,25272,3841],{"className":25273,"style":3866},[1844,1845],[1788,25275],{"className":25276,"style":1851},[1850],[1788,25278,15270],{"className":25279},[1855],[1788,25281],{"className":25282,"style":1851},[1850],[1788,25284,25286,25290,25322,25325,25328],{"className":25285},[1835],[1788,25287],{"className":25288,"style":25289},[1839],"height:0.8491em;",[1788,25291,25293,25296],{"className":25292},[1844],[1788,25294,2290],{"className":25295},[1844,1845],[1788,25297,25299],{"className":25298},[1875],[1788,25300,25302],{"className":25301},[1879],[1788,25303,25305],{"className":25304},[1883],[1788,25306,25308],{"className":25307,"style":25289},[1887],[1788,25309,25310,25313],{"style":1890},[1788,25311],{"className":25312,"style":1895},[1894],[1788,25314,25316],{"className":25315},[1899,1900,1901,1902],[1788,25317,25319],{"className":25318},[1844,1902],[1788,25320,1938],{"className":25321,"style":1954},[1844,1845,1902],[1788,25323],{"className":25324,"style":1851},[1850],[1788,25326,6081],{"className":25327},[1855],[1788,25329],{"className":25330,"style":1851},[1850],[1788,25332,25334,25338,25370,25373,25376,25379,25383,25386,25389,25392,25395,25398],{"className":25333},[1835],[1788,25335],{"className":25336,"style":25337},[1839],"height:1.0991em;vertical-align:-0.25em;",[1788,25339,25341,25344],{"className":25340},[1844],[1788,25342,3841],{"className":25343,"style":3866},[1844,1845],[1788,25345,25347],{"className":25346},[1875],[1788,25348,25350],{"className":25349},[1879],[1788,25351,25353],{"className":25352},[1883],[1788,25354,25356],{"className":25355,"style":25289},[1887],[1788,25357,25358,25361],{"style":1890},[1788,25359],{"className":25360,"style":1895},[1894],[1788,25362,25364],{"className":25363},[1899,1900,1901,1902],[1788,25365,25367],{"className":25366},[1844,1902],[1788,25368,1938],{"className":25369,"style":1954},[1844,1845,1902],[1788,25371,2430],{"className":25372},[2474],[1788,25374,1973],{"className":25375},[1850],[1788,25377],{"className":25378,"style":2478},[1850],[1788,25380,25224],{"className":25381,"style":25382},[1844,1845],"margin-right:0.1076em;",[1788,25384,1977],{"className":25385},[2013],[1788,25387,2290],{"className":25388},[1844,1845],[1788,25390,1990],{"className":25391},[2079],[1788,25393],{"className":25394,"style":1851},[1850],[1788,25396,6081],{"className":25397},[1855],[1788,25399],{"className":25400,"style":1851},[1850],[1788,25402,25404,25407,25410,25413,25416],{"className":25403},[1835],[1788,25405],{"className":25406,"style":2003},[1839],[1788,25408,25224],{"className":25409,"style":25382},[1844,1845],[1788,25411,1977],{"className":25412},[2013],[1788,25414,3841],{"className":25415,"style":3866},[1844,1845],[1788,25417,1990],{"className":25418},[2079],"；\n② 若 ",[1788,25421,25423,25440],{"className":25422},[1791],[1788,25424,25426],{"className":25425},[1795],[1797,25427,25428],{"xmlns":1799},[1801,25429,25430,25438],{},[1804,25431,25432,25434,25436],{},[1807,25433,2290],{},[1811,25435,6081],{},[1807,25437,3841],{},[1823,25439,21517],{"encoding":1825},[1788,25441,25443,25461],{"className":25442,"ariaHidden":1831},[1830],[1788,25444,25446,25449,25452,25455,25458],{"className":25445},[1835],[1788,25447],{"className":25448,"style":1840},[1839],[1788,25450,2290],{"className":25451},[1844,1845],[1788,25453],{"className":25454,"style":1851},[1850],[1788,25456,6081],{"className":25457},[1855],[1788,25459],{"className":25460,"style":1851},[1850],[1788,25462,25464,25467],{"className":25463},[1835],[1788,25465],{"className":25466,"style":1840},[1839],[1788,25468,3841],{"className":25469,"style":3866},[1844,1845],[1788,25471,25473,25486],{"className":25472},[1791],[1788,25474,25476],{"className":25475},[1795],[1797,25477,25478],{"xmlns":1799},[1801,25479,25480,25484],{},[1804,25481,25482],{},[1807,25483,2290],{},[1823,25485,2290],{"encoding":1825},[1788,25487,25489],{"className":25488,"ariaHidden":1831},[1830],[1788,25490,25492,25495],{"className":25491},[1835],[1788,25493],{"className":25494,"style":1840},[1839],[1788,25496,2290],{"className":25497},[1844,1845]," 可逆，则 ",[1788,25500,25502,25574],{"className":25501},[1791],[1788,25503,25505],{"className":25504},[1795],[1797,25506,25507],{"xmlns":1799},[1801,25508,25509,25571],{},[1804,25510,25511,25521,25523,25533,25535,25537,25539,25541,25551,25553,25555,25557,25559,25569],{},[1815,25512,25513,25515],{},[1807,25514,2290],{},[1804,25516,25517,25519],{},[1811,25518,3250],{},[1985,25520,2906],{},[1811,25522,6081],{},[1815,25524,25525,25527],{},[1807,25526,3841],{},[1804,25528,25529,25531],{},[1811,25530,3250],{},[1985,25532,2906],{},[1811,25534,2430],{"separator":1831},[1971,25536,1973],{},[1807,25538,25224],{},[1811,25540,1977],{"stretchy":1976},[1815,25542,25543,25545],{},[1807,25544,2290],{},[1804,25546,25547,25549],{},[1811,25548,3250],{},[1985,25550,2906],{},[1811,25552,1990],{"stretchy":1976},[1811,25554,6081],{},[1807,25556,25224],{},[1811,25558,1977],{"stretchy":1976},[1815,25560,25561,25563],{},[1807,25562,3841],{},[1804,25564,25565,25567],{},[1811,25566,3250],{},[1985,25568,2906],{},[1811,25570,1990],{"stretchy":1976},[1823,25572,25573],{"encoding":1825},"A^{-1}\\sim B^{-1},\\ f(A^{-1})\\sim f(B^{-1})",[1788,25575,25577,25627,25731],{"className":25576,"ariaHidden":1831},[1830],[1788,25578,25580,25583,25618,25621,25624],{"className":25579},[1835],[1788,25581],{"className":25582,"style":3265},[1839],[1788,25584,25586,25589],{"className":25585},[1844],[1788,25587,2290],{"className":25588},[1844,1845],[1788,25590,25592],{"className":25591},[1875],[1788,25593,25595],{"className":25594},[1879],[1788,25596,25598],{"className":25597},[1883],[1788,25599,25601],{"className":25600,"style":3265},[1887],[1788,25602,25603,25606],{"style":1890},[1788,25604],{"className":25605,"style":1895},[1894],[1788,25607,25609],{"className":25608},[1899,1900,1901,1902],[1788,25610,25612,25615],{"className":25611},[1844,1902],[1788,25613,3250],{"className":25614},[1844,1902],[1788,25616,2906],{"className":25617},[1844,1902],[1788,25619],{"className":25620,"style":1851},[1850],[1788,25622,6081],{"className":25623},[1855],[1788,25625],{"className":25626,"style":1851},[1850],[1788,25628,25630,25634,25669,25672,25675,25678,25681,25684,25719,25722,25725,25728],{"className":25629},[1835],[1788,25631],{"className":25632,"style":25633},[1839],"height:1.0641em;vertical-align:-0.25em;",[1788,25635,25637,25640],{"className":25636},[1844],[1788,25638,3841],{"className":25639,"style":3866},[1844,1845],[1788,25641,25643],{"className":25642},[1875],[1788,25644,25646],{"className":25645},[1879],[1788,25647,25649],{"className":25648},[1883],[1788,25650,25652],{"className":25651,"style":3265},[1887],[1788,25653,25654,25657],{"style":1890},[1788,25655],{"className":25656,"style":1895},[1894],[1788,25658,25660],{"className":25659},[1899,1900,1901,1902],[1788,25661,25663,25666],{"className":25662},[1844,1902],[1788,25664,3250],{"className":25665},[1844,1902],[1788,25667,2906],{"className":25668},[1844,1902],[1788,25670,2430],{"className":25671},[2474],[1788,25673,1973],{"className":25674},[1850],[1788,25676],{"className":25677,"style":2478},[1850],[1788,25679,25224],{"className":25680,"style":25382},[1844,1845],[1788,25682,1977],{"className":25683},[2013],[1788,25685,25687,25690],{"className":25686},[1844],[1788,25688,2290],{"className":25689},[1844,1845],[1788,25691,25693],{"className":25692},[1875],[1788,25694,25696],{"className":25695},[1879],[1788,25697,25699],{"className":25698},[1883],[1788,25700,25702],{"className":25701,"style":3265},[1887],[1788,25703,25704,25707],{"style":1890},[1788,25705],{"className":25706,"style":1895},[1894],[1788,25708,25710],{"className":25709},[1899,1900,1901,1902],[1788,25711,25713,25716],{"className":25712},[1844,1902],[1788,25714,3250],{"className":25715},[1844,1902],[1788,25717,2906],{"className":25718},[1844,1902],[1788,25720,1990],{"className":25721},[2079],[1788,25723],{"className":25724,"style":1851},[1850],[1788,25726,6081],{"className":25727},[1855],[1788,25729],{"className":25730,"style":1851},[1850],[1788,25732,25734,25737,25740,25743,25778],{"className":25733},[1835],[1788,25735],{"className":25736,"style":25633},[1839],[1788,25738,25224],{"className":25739,"style":25382},[1844,1845],[1788,25741,1977],{"className":25742},[2013],[1788,25744,25746,25749],{"className":25745},[1844],[1788,25747,3841],{"className":25748,"style":3866},[1844,1845],[1788,25750,25752],{"className":25751},[1875],[1788,25753,25755],{"className":25754},[1879],[1788,25756,25758],{"className":25757},[1883],[1788,25759,25761],{"className":25760,"style":3265},[1887],[1788,25762,25763,25766],{"style":1890},[1788,25764],{"className":25765,"style":1895},[1894],[1788,25767,25769],{"className":25768},[1899,1900,1901,1902],[1788,25770,25772,25775],{"className":25771},[1844,1902],[1788,25773,3250],{"className":25774},[1844,1902],[1788,25776,2906],{"className":25777},[1844,1902],[1788,25779,1990],{"className":25780},[2079],"；\n③ 若 ",[1788,25783,25785,25802],{"className":25784},[1791],[1788,25786,25788],{"className":25787},[1795],[1797,25789,25790],{"xmlns":1799},[1801,25791,25792,25800],{},[1804,25793,25794,25796,25798],{},[1807,25795,2290],{},[1811,25797,6081],{},[1807,25799,3841],{},[1823,25801,21517],{"encoding":1825},[1788,25803,25805,25823],{"className":25804,"ariaHidden":1831},[1830],[1788,25806,25808,25811,25814,25817,25820],{"className":25807},[1835],[1788,25809],{"className":25810,"style":1840},[1839],[1788,25812,2290],{"className":25813},[1844,1845],[1788,25815],{"className":25816,"style":1851},[1850],[1788,25818,6081],{"className":25819},[1855],[1788,25821],{"className":25822,"style":1851},[1850],[1788,25824,25826,25829],{"className":25825},[1835],[1788,25827],{"className":25828,"style":1840},[1839],[1788,25830,3841],{"className":25831,"style":3866},[1844,1845],[1788,25833,25835,25861],{"className":25834},[1791],[1788,25836,25838],{"className":25837},[1795],[1797,25839,25840],{"xmlns":1799},[1801,25841,25842,25858],{},[1804,25843,25844,25850,25852],{},[1815,25845,25846,25848],{},[1807,25847,2290],{},[1811,25849,7136],{"lspace":7135,"rspace":7135},[1811,25851,6081],{},[1815,25853,25854,25856],{},[1807,25855,3841],{},[1811,25857,7136],{"lspace":7135,"rspace":7135},[1823,25859,25860],{"encoding":1825},"A^{*}\\sim B^{*}",[1788,25862,25864,25911],{"className":25863,"ariaHidden":1831},[1830],[1788,25865,25867,25870,25902,25905,25908],{"className":25866},[1835],[1788,25868],{"className":25869,"style":7179},[1839],[1788,25871,25873,25876],{"className":25872},[1844],[1788,25874,2290],{"className":25875},[1844,1845],[1788,25877,25879],{"className":25878},[1875],[1788,25880,25882],{"className":25881},[1879],[1788,25883,25885],{"className":25884},[1883],[1788,25886,25888],{"className":25887,"style":7179},[1887],[1788,25889,25890,25893],{"style":1890},[1788,25891],{"className":25892,"style":1895},[1894],[1788,25894,25896],{"className":25895},[1899,1900,1901,1902],[1788,25897,25899],{"className":25898},[1844,1902],[1788,25900,7136],{"className":25901},[1844,1902],[1788,25903],{"className":25904,"style":1851},[1850],[1788,25906,6081],{"className":25907},[1855],[1788,25909],{"className":25910,"style":1851},[1850],[1788,25912,25914,25917],{"className":25913},[1835],[1788,25915],{"className":25916,"style":7179},[1839],[1788,25918,25920,25923],{"className":25919},[1844],[1788,25921,3841],{"className":25922,"style":3866},[1844,1845],[1788,25924,25926],{"className":25925},[1875],[1788,25927,25929],{"className":25928},[1879],[1788,25930,25932],{"className":25931},[1883],[1788,25933,25935],{"className":25934,"style":7179},[1887],[1788,25936,25937,25940],{"style":1890},[1788,25938],{"className":25939,"style":1895},[1894],[1788,25941,25943],{"className":25942},[1899,1900,1901,1902],[1788,25944,25946],{"className":25945},[1844,1902],[1788,25947,7136],{"className":25948},[1844,1902],[1788,25950,25952,25969],{"className":25951},[1791],[1788,25953,25955],{"className":25954},[1795],[1797,25956,25957],{"xmlns":1799},[1801,25958,25959,25967],{},[1804,25960,25961,25963,25965],{},[1807,25962,2290],{},[1811,25964,2430],{"separator":1831},[1807,25966,3841],{},[1823,25968,8906],{"encoding":1825},[1788,25970,25972],{"className":25971,"ariaHidden":1831},[1830],[1788,25973,25975,25978,25981,25984,25987],{"className":25974},[1835],[1788,25976],{"className":25977,"style":7685},[1839],[1788,25979,2290],{"className":25980},[1844,1845],[1788,25982,2430],{"className":25983},[2474],[1788,25985],{"className":25986,"style":2478},[1850],[1788,25988,3841],{"className":25989,"style":3866},[1844,1845]," 可逆时）；\n④ 若 ",[1788,25992,25994,26011],{"className":25993},[1791],[1788,25995,25997],{"className":25996},[1795],[1797,25998,25999],{"xmlns":1799},[1801,26000,26001,26009],{},[1804,26002,26003,26005,26007],{},[1807,26004,2290],{},[1811,26006,6081],{},[1807,26008,3841],{},[1823,26010,21517],{"encoding":1825},[1788,26012,26014,26032],{"className":26013,"ariaHidden":1831},[1830],[1788,26015,26017,26020,26023,26026,26029],{"className":26016},[1835],[1788,26018],{"className":26019,"style":1840},[1839],[1788,26021,2290],{"className":26022},[1844,1845],[1788,26024],{"className":26025,"style":1851},[1850],[1788,26027,6081],{"className":26028},[1855],[1788,26030],{"className":26031,"style":1851},[1850],[1788,26033,26035,26038],{"className":26034},[1835],[1788,26036],{"className":26037,"style":1840},[1839],[1788,26039,3841],{"className":26040,"style":3866},[1844,1845],[1788,26042,26044,26070],{"className":26043},[1791],[1788,26045,26047],{"className":26046},[1795],[1797,26048,26049],{"xmlns":1799},[1801,26050,26051,26067],{},[1804,26052,26053,26059,26061],{},[1815,26054,26055,26057],{},[1807,26056,2290],{},[1807,26058,1821],{},[1811,26060,6081],{},[1815,26062,26063,26065],{},[1807,26064,3841],{},[1807,26066,1821],{},[1823,26068,26069],{"encoding":1825},"A^{T}\\sim B^{T}",[1788,26071,26073,26120],{"className":26072,"ariaHidden":1831},[1830],[1788,26074,26076,26079,26111,26114,26117],{"className":26075},[1835],[1788,26077],{"className":26078,"style":1865},[1839],[1788,26080,26082,26085],{"className":26081},[1844],[1788,26083,2290],{"className":26084},[1844,1845],[1788,26086,26088],{"className":26087},[1875],[1788,26089,26091],{"className":26090},[1879],[1788,26092,26094],{"className":26093},[1883],[1788,26095,26097],{"className":26096,"style":1865},[1887],[1788,26098,26099,26102],{"style":1890},[1788,26100],{"className":26101,"style":1895},[1894],[1788,26103,26105],{"className":26104},[1899,1900,1901,1902],[1788,26106,26108],{"className":26107},[1844,1902],[1788,26109,1821],{"className":26110,"style":1909},[1844,1845,1902],[1788,26112],{"className":26113,"style":1851},[1850],[1788,26115,6081],{"className":26116},[1855],[1788,26118],{"className":26119,"style":1851},[1850],[1788,26121,26123,26126],{"className":26122},[1835],[1788,26124],{"className":26125,"style":1865},[1839],[1788,26127,26129,26132],{"className":26128},[1844],[1788,26130,3841],{"className":26131,"style":3866},[1844,1845],[1788,26133,26135],{"className":26134},[1875],[1788,26136,26138],{"className":26137},[1879],[1788,26139,26141],{"className":26140},[1883],[1788,26142,26144],{"className":26143,"style":1865},[1887],[1788,26145,26146,26149],{"style":1890},[1788,26147],{"className":26148,"style":1895},[1894],[1788,26150,26152],{"className":26151},[1899,1900,1901,1902],[1788,26153,26155],{"className":26154},[1844,1902],[1788,26156,1821],{"className":26157,"style":1909},[1844,1845,1902],[1096,26159,26160],{},[2114,26161],{"alt":26162,"src":26163},"相似结论补充","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be22f103e.png",[1096,26165,26166],{},[1099,26167,26168],{},"注：",[1096,26170,26171],{},[2114,26172],{"alt":26173,"src":26174},"相似之注","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be23741bd.png",[1091,26176,26178],{"id":26177},"十-合同","十. 合同",[1096,26180,4867,26181,5157,26222,26250,26251,9061,26281,21438,26375,8852,26403,26431,26432,2389,26484,8852,26512,26540,26541,26544,26545,26548],{},[1788,26182,26184,26201],{"className":26183},[1791],[1788,26185,26187],{"className":26186},[1795],[1797,26188,26189],{"xmlns":1799},[1801,26190,26191,26199],{},[1804,26192,26193,26195,26197],{},[1807,26194,2290],{},[1811,26196,2430],{"separator":1831},[1807,26198,3841],{},[1823,26200,8906],{"encoding":1825},[1788,26202,26204],{"className":26203,"ariaHidden":1831},[1830],[1788,26205,26207,26210,26213,26216,26219],{"className":26206},[1835],[1788,26208],{"className":26209,"style":7685},[1839],[1788,26211,2290],{"className":26212},[1844,1845],[1788,26214,2430],{"className":26215},[2474],[1788,26217],{"className":26218,"style":2478},[1850],[1788,26220,3841],{"className":26221,"style":3866},[1844,1845],[1788,26223,26225,26238],{"className":26224},[1791],[1788,26226,26228],{"className":26227},[1795],[1797,26229,26230],{"xmlns":1799},[1801,26231,26232,26236],{},[1804,26233,26234],{},[1807,26235,2301],{},[1823,26237,2301],{"encoding":1825},[1788,26239,26241],{"className":26240,"ariaHidden":1831},[1830],[1788,26242,26244,26247],{"className":26243},[1835],[1788,26245],{"className":26246,"style":3114},[1839],[1788,26248,2301],{"className":26249},[1844,1845]," 阶矩阵，若存在可逆矩阵 ",[1788,26252,26254,26268],{"className":26253},[1791],[1788,26255,26257],{"className":26256},[1795],[1797,26258,26259],{"xmlns":1799},[1801,26260,26261,26266],{},[1804,26262,26263],{},[1807,26264,26265],{},"C",[1823,26267,26265],{"encoding":1825},[1788,26269,26271],{"className":26270,"ariaHidden":1831},[1830],[1788,26272,26274,26277],{"className":26273},[1835],[1788,26275],{"className":26276,"style":1840},[1839],[1788,26278,26265],{"className":26279,"style":26280},[1844,1845],"margin-right:0.0715em;",[1788,26282,26284,26310],{"className":26283},[1791],[1788,26285,26287],{"className":26286},[1795],[1797,26288,26289],{"xmlns":1799},[1801,26290,26291,26307],{},[1804,26292,26293,26299,26301,26303,26305],{},[1815,26294,26295,26297],{},[1807,26296,26265],{},[1807,26298,1821],{},[1807,26300,2290],{},[1807,26302,26265],{},[1811,26304,1813],{},[1807,26306,3841],{},[1823,26308,26309],{"encoding":1825},"C^{T}AC=B",[1788,26311,26313,26366],{"className":26312,"ariaHidden":1831},[1830],[1788,26314,26316,26319,26351,26354,26357,26360,26363],{"className":26315},[1835],[1788,26317],{"className":26318,"style":1865},[1839],[1788,26320,26322,26325],{"className":26321},[1844],[1788,26323,26265],{"className":26324,"style":26280},[1844,1845],[1788,26326,26328],{"className":26327},[1875],[1788,26329,26331],{"className":26330},[1879],[1788,26332,26334],{"className":26333},[1883],[1788,26335,26337],{"className":26336,"style":1865},[1887],[1788,26338,26339,26342],{"style":1890},[1788,26340],{"className":26341,"style":1895},[1894],[1788,26343,26345],{"className":26344},[1899,1900,1901,1902],[1788,26346,26348],{"className":26347},[1844,1902],[1788,26349,1821],{"className":26350,"style":1909},[1844,1845,1902],[1788,26352,2290],{"className":26353},[1844,1845],[1788,26355,26265],{"className":26356,"style":26280},[1844,1845],[1788,26358],{"className":26359,"style":1851},[1850],[1788,26361,1813],{"className":26362},[1855],[1788,26364],{"className":26365,"style":1851},[1850],[1788,26367,26369,26372],{"className":26368},[1835],[1788,26370],{"className":26371,"style":1840},[1839],[1788,26373,3841],{"className":26374,"style":3866},[1844,1845],[1788,26376,26378,26391],{"className":26377},[1791],[1788,26379,26381],{"className":26380},[1795],[1797,26382,26383],{"xmlns":1799},[1801,26384,26385,26389],{},[1804,26386,26387],{},[1807,26388,2290],{},[1823,26390,2290],{"encoding":1825},[1788,26392,26394],{"className":26393,"ariaHidden":1831},[1830],[1788,26395,26397,26400],{"className":26396},[1835],[1788,26398],{"className":26399,"style":1840},[1839],[1788,26401,2290],{"className":26402},[1844,1845],[1788,26404,26406,26419],{"className":26405},[1791],[1788,26407,26409],{"className":26408},[1795],[1797,26410,26411],{"xmlns":1799},[1801,26412,26413,26417],{},[1804,26414,26415],{},[1807,26416,3841],{},[1823,26418,3841],{"encoding":1825},[1788,26420,26422],{"className":26421,"ariaHidden":1831},[1830],[1788,26423,26425,26428],{"className":26424},[1835],[1788,26426],{"className":26427,"style":1840},[1839],[1788,26429,3841],{"className":26430,"style":3866},[1844,1845]," 合同，即 ",[1788,26433,26435,26454],{"className":26434},[1791],[1788,26436,26438],{"className":26437},[1795],[1797,26439,26440],{"xmlns":1799},[1801,26441,26442,26451],{},[1804,26443,26444,26446,26449],{},[1807,26445,2290],{},[1811,26447,26448],{},"≅",[1807,26450,3841],{},[1823,26452,26453],{"encoding":1825},"A\\cong B",[1788,26455,26457,26475],{"className":26456,"ariaHidden":1831},[1830],[1788,26458,26460,26463,26466,26469,26472],{"className":26459},[1835],[1788,26461],{"className":26462,"style":1840},[1839],[1788,26464,2290],{"className":26465},[1844,1845],[1788,26467],{"className":26468,"style":1851},[1850],[1788,26470,26448],{"className":26471},[1855],[1788,26473],{"className":26474,"style":1851},[1850],[1788,26476,26478,26481],{"className":26477},[1835],[1788,26479],{"className":26480,"style":1840},[1839],[1788,26482,3841],{"className":26483,"style":3866},[1844,1845],[1788,26485,26487,26500],{"className":26486},[1791],[1788,26488,26490],{"className":26489},[1795],[1797,26491,26492],{"xmlns":1799},[1801,26493,26494,26498],{},[1804,26495,26496],{},[1807,26497,2290],{},[1823,26499,2290],{"encoding":1825},[1788,26501,26503],{"className":26502,"ariaHidden":1831},[1830],[1788,26504,26506,26509],{"className":26505},[1835],[1788,26507],{"className":26508,"style":1840},[1839],[1788,26510,2290],{"className":26511},[1844,1845],[1788,26513,26515,26528],{"className":26514},[1791],[1788,26516,26518],{"className":26517},[1795],[1797,26519,26520],{"xmlns":1799},[1801,26521,26522,26526],{},[1804,26523,26524],{},[1807,26525,3841],{},[1823,26527,3841],{"encoding":1825},[1788,26529,26531],{"className":26530,"ariaHidden":1831},[1830],[1788,26532,26534,26537],{"className":26533},[1835],[1788,26535],{"className":26536,"style":1840},[1839],[1788,26538,3841],{"className":26539,"style":3866},[1844,1845]," 合同，就是指同一个",[1099,26542,26543],{},"二次型","在",[1099,26546,26547],{},"可逆线性变换","下的两个不同状态的联系。",[1096,26550,26551],{},[2114,26552],{"alt":26553,"src":26554},"合同（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be23716ca.png",[1096,26556,26557],{},[2114,26558],{"alt":26559,"src":26560},"合同（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be23c6528.png",[1096,26562,26563],{},[2114,26564],{"alt":26565,"src":26566},"合同（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be240b87e.png",[1096,26568,26569],{},"**注：**由于我们已经规定，对称矩阵才是二次型矩阵，所以二次型矩阵都是对称矩阵，相应的和对称矩阵合同的矩阵也是对称矩阵。",[1096,26571,26572],{},[1099,26573,11292],{},[1096,26575,26576],{},[2114,26577],{"alt":26578,"src":26579},"合同例题（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be23c6692.png",[1096,26581,26582],{},[2114,26583],{"alt":26584,"src":26585},"合同例题（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be245dd6f.png",[1096,26587,26588],{},[2114,26589],{"alt":26590,"src":26591},"合同例题（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be24aba92.png",[1096,26593,26594],{},[2114,26595],{"alt":26596,"src":26597},"合同例题（四）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be24a8cd1.png",[1091,26599,26601],{"id":26600},"十一-二次型","十一. 二次型",[1096,26603,26604],{},"关于二次型化标准型或规范型的方法（配方法、正交变换）总结如下：",[1096,26606,26607],{},[2114,26608],{"alt":26609,"src":26610},"二次型化标准型","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be260b287.png",[1096,26612,26613],{},[1099,26614,26615],{},"所以我们可以进一步得到等价、合同和相似的关系：",[1096,26617,26618],{},[2114,26619],{"alt":26620,"src":26621},"等价、合同、相似的关系","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be26b3cd5.png",[1096,26623,26624,26625,26666],{},"**注：**相似一定合同的前提条件是 ",[1788,26626,26628,26645],{"className":26627},[1791],[1788,26629,26631],{"className":26630},[1795],[1797,26632,26633],{"xmlns":1799},[1801,26634,26635,26643],{},[1804,26636,26637,26639,26641],{},[1807,26638,2290],{},[1811,26640,2430],{"separator":1831},[1807,26642,3841],{},[1823,26644,8906],{"encoding":1825},[1788,26646,26648],{"className":26647,"ariaHidden":1831},[1830],[1788,26649,26651,26654,26657,26660,26663],{"className":26650},[1835],[1788,26652],{"className":26653,"style":7685},[1839],[1788,26655,2290],{"className":26656},[1844,1845],[1788,26658,2430],{"className":26659},[2474],[1788,26661],{"className":26662,"style":2478},[1850],[1788,26664,3841],{"className":26665,"style":3866},[1844,1845]," 都是实对称矩阵。",[1096,26668,26669],{},[2114,26670],{"alt":26671,"src":26672},"相似与合同之注","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2634cf1.png",[1096,26674,26675],{},[1099,26676,11292],{},[1096,26678,26679],{},[2114,26680],{"alt":26681,"src":26682},"二次型例题（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be265a9df.png",[1096,26684,26685],{},[2114,26686],{"alt":26687,"src":26688},"二次型例题（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be27a8028.png",[1096,26690,26691],{},"关于配方法和正交变换分别给一个例题：",[1096,26693,26694],{},[1099,26695,26696],{},"配方法：",[1096,26698,26699],{},[2114,26700],{"alt":26701,"src":26702},"配方法例题","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be28c1744.png",[1096,26704,26705],{},[1099,26706,26707],{},"正交变换：",[1096,26709,26710],{},[2114,26711],{"alt":26712,"src":26713},"正交变换例题（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be27ea985.png",[1096,26715,26716],{},[2114,26717],{"alt":26718,"src":26719},"正交变换例题（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be27d854c.png",[1912,26721,26722],{},[1096,26723,15855,26724,26857,26858,27120],{},[1788,26725,26727,26753],{"className":26726},[1791],[1788,26728,26730],{"className":26729},[1795],[1797,26731,26732],{"xmlns":1799},[1801,26733,26734,26750],{},[1804,26735,26736,26742,26744],{},[2881,26737,26738,26740],{},[1807,26739,20664],{},[1985,26741,2906],{},[1811,26743,1813],{},[2881,26745,26746,26748],{},[1807,26747,20664],{},[1985,26749,2896],{},[1823,26751,26752],{"encoding":1825},"\\lambda_1=\\lambda_2",[1788,26754,26756,26811],{"className":26755,"ariaHidden":1831},[1830],[1788,26757,26759,26762,26802,26805,26808],{"className":26758},[1835],[1788,26760],{"className":26761,"style":17730},[1839],[1788,26763,26765,26768],{"className":26764},[1844],[1788,26766,20664],{"className":26767},[1844,1845],[1788,26769,26771],{"className":26770},[1875],[1788,26772,26774,26794],{"className":26773},[1879,2931],[1788,26775,26777,26791],{"className":26776},[1883],[1788,26778,26780],{"className":26779,"style":2938},[1887],[1788,26781,26782,26785],{"style":4072},[1788,26783],{"className":26784,"style":1895},[1894],[1788,26786,26788],{"className":26787},[1899,1900,1901,1902],[1788,26789,2906],{"className":26790},[1844,1902],[1788,26792,2958],{"className":26793},[2957],[1788,26795,26797],{"className":26796},[1883],[1788,26798,26800],{"className":26799,"style":2965},[1887],[1788,26801],{},[1788,26803],{"className":26804,"style":1851},[1850],[1788,26806,1813],{"className":26807},[1855],[1788,26809],{"className":26810,"style":1851},[1850],[1788,26812,26814,26817],{"className":26813},[1835],[1788,26815],{"className":26816,"style":17730},[1839],[1788,26818,26820,26823],{"className":26819},[1844],[1788,26821,20664],{"className":26822},[1844,1845],[1788,26824,26826],{"className":26825},[1875],[1788,26827,26829,26849],{"className":26828},[1879,2931],[1788,26830,26832,26846],{"className":26831},[1883],[1788,26833,26835],{"className":26834,"style":2938},[1887],[1788,26836,26837,26840],{"style":4072},[1788,26838],{"className":26839,"style":1895},[1894],[1788,26841,26843],{"className":26842},[1899,1900,1901,1902],[1788,26844,2896],{"className":26845},[1844,1902],[1788,26847,2958],{"className":26848},[2957],[1788,26850,26852],{"className":26851},[1883],[1788,26853,26855],{"className":26854,"style":2965},[1887],[1788,26856],{},"，那么两个同一特征值对应的特征向量需要正交化；如果本来就正交可以不做这一步，所以在计算特征值的时候，可以将两个特征向量写为正交的，这样就免去了施密特正交化，直接进入单位化即可。\n② ",[1788,26859,26861,26895],{"className":26860},[1791],[1788,26862,26864],{"className":26863},[1795],[1797,26865,26866],{"xmlns":1799},[1801,26867,26868,26892],{},[1804,26869,26870,26876,26878,26884,26886],{},[2881,26871,26872,26874],{},[1807,26873,20664],{},[1985,26875,2906],{},[1811,26877,1983],{"mathvariant":1982},[2881,26879,26880,26882],{},[1807,26881,20664],{},[1985,26883,2896],{},[1811,26885,1983],{"mathvariant":1982},[2881,26887,26888,26890],{},[1807,26889,20664],{},[1985,26891,2887],{},[1823,26893,26894],{"encoding":1825},"\\lambda_1\\neq\\lambda_2\\neq\\lambda_3",[1788,26896,26898,26986,27074],{"className":26897,"ariaHidden":1831},[1830],[1788,26899,26901,26904,26944,26947,26983],{"className":26900},[1835],[1788,26902],{"className":26903,"style":2041},[1839],[1788,26905,26907,26910],{"className":26906},[1844],[1788,26908,20664],{"className":26909},[1844,1845],[1788,26911,26913],{"className":26912},[1875],[1788,26914,26916,26936],{"className":26915},[1879,2931],[1788,26917,26919,26933],{"className":26918},[1883],[1788,26920,26922],{"className":26921,"style":2938},[1887],[1788,26923,26924,26927],{"style":4072},[1788,26925],{"className":26926,"style":1895},[1894],[1788,26928,26930],{"className":26929},[1899,1900,1901,1902],[1788,26931,2906],{"className":26932},[1844,1902],[1788,26934,2958],{"className":26935},[2957],[1788,26937,26939],{"className":26938},[1883],[1788,26940,26942],{"className":26941,"style":2965},[1887],[1788,26943],{},[1788,26945],{"className":26946,"style":1851},[1850],[1788,26948,26950,26977,26980],{"className":26949},[1855],[1788,26951,26953],{"className":26952},[1855],[1788,26954,26956],{"className":26955},[1844,2029],[1788,26957,26959],{"className":26958},[2033],[1788,26960,26962,26965,26974],{"className":26961},[2037],[1788,26963],{"className":26964,"style":2041},[1839],[1788,26966,26968],{"className":26967},[2045],[1788,26969,26971],{"className":26970},[1844],[1788,26972,2052],{"className":26973},[1855],[1788,26975],{"className":26976},[2056],[1788,26978],{"className":26979},[1850,2060],[1788,26981,1813],{"className":26982},[1855],[1788,26984],{"className":26985,"style":1851},[1850],[1788,26987,26989,26992,27032,27035,27071],{"className":26988},[1835],[1788,26990],{"className":26991,"style":2041},[1839],[1788,26993,26995,26998],{"className":26994},[1844],[1788,26996,20664],{"className":26997},[1844,1845],[1788,26999,27001],{"className":27000},[1875],[1788,27002,27004,27024],{"className":27003},[1879,2931],[1788,27005,27007,27021],{"className":27006},[1883],[1788,27008,27010],{"className":27009,"style":2938},[1887],[1788,27011,27012,27015],{"style":4072},[1788,27013],{"className":27014,"style":1895},[1894],[1788,27016,27018],{"className":27017},[1899,1900,1901,1902],[1788,27019,2896],{"className":27020},[1844,1902],[1788,27022,2958],{"className":27023},[2957],[1788,27025,27027],{"className":27026},[1883],[1788,27028,27030],{"className":27029,"style":2965},[1887],[1788,27031],{},[1788,27033],{"className":27034,"style":1851},[1850],[1788,27036,27038,27065,27068],{"className":27037},[1855],[1788,27039,27041],{"className":27040},[1855],[1788,27042,27044],{"className":27043},[1844,2029],[1788,27045,27047],{"className":27046},[2033],[1788,27048,27050,27053,27062],{"className":27049},[2037],[1788,27051],{"className":27052,"style":2041},[1839],[1788,27054,27056],{"className":27055},[2045],[1788,27057,27059],{"className":27058},[1844],[1788,27060,2052],{"className":27061},[1855],[1788,27063],{"className":27064},[2056],[1788,27066],{"className":27067},[1850,2060],[1788,27069,1813],{"className":27070},[1855],[1788,27072],{"className":27073,"style":1851},[1850],[1788,27075,27077,27080],{"className":27076},[1835],[1788,27078],{"className":27079,"style":17730},[1839],[1788,27081,27083,27086],{"className":27082},[1844],[1788,27084,20664],{"className":27085},[1844,1845],[1788,27087,27089],{"className":27088},[1875],[1788,27090,27092,27112],{"className":27091},[1879,2931],[1788,27093,27095,27109],{"className":27094},[1883],[1788,27096,27098],{"className":27097,"style":2938},[1887],[1788,27099,27100,27103],{"style":4072},[1788,27101],{"className":27102,"style":1895},[1894],[1788,27104,27106],{"className":27105},[1899,1900,1901,1902],[1788,27107,2887],{"className":27108},[1844,1902],[1788,27110,2958],{"className":27111},[2957],[1788,27113,27115],{"className":27114},[1883],[1788,27116,27118],{"className":27117,"style":2965},[1887],[1788,27119],{},"，那么不用进行施密特正交化，直接单位化即可。",[1096,27122,27123],{},[1099,27124,27125],{},"常见题型：",[1096,27127,27128],{},[2114,27129],{"alt":27130,"src":27131},"二次型常见题型（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be27a8802.png",[1096,27133,27134],{},[2114,27135],{"alt":27136,"src":27137},"二次型常见题型（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be28ccb91.png",[1096,27139,27140],{},"这里记录一个例题：",[1096,27142,27143],{},[2114,27144],{"alt":27145,"src":27146},"二次型例题（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be29b50e6.png",[1096,27148,27149],{},[2114,27150],{"alt":27151,"src":27152},"二次型例题（四）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be29d5c66.png",[1096,27154,27155],{},"若二次型中只有混合项，没有平方项，要怎么做？",[1096,27157,27158],{},[2114,27159],{"alt":27160,"src":27161},"只有混合项的处理","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2a51d99.png",[1091,27163,27165],{"id":27164},"十二-二次型正定","十二. 二次型正定",[1912,27167,27168,27173,27509,27903,27906,27912],{},[1096,27169,27170],{},[1099,27171,27172],{},"二次型正定的充要条件：",[1096,27174,27175,27203,27204,27298,27299,27327,27328,24874,27412,27508],{},[1788,27176,27178,27191],{"className":27177},[1791],[1788,27179,27181],{"className":27180},[1795],[1797,27182,27183],{"xmlns":1799},[1801,27184,27185,27189],{},[1804,27186,27187],{},[1807,27188,2301],{},[1823,27190,2301],{"encoding":1825},[1788,27192,27194],{"className":27193,"ariaHidden":1831},[1830],[1788,27195,27197,27200],{"className":27196},[1835],[1788,27198],{"className":27199,"style":3114},[1839],[1788,27201,2301],{"className":27202},[1844,1845]," 元二次型 ",[1788,27205,27207,27233],{"className":27206},[1791],[1788,27208,27210],{"className":27209},[1795],[1797,27211,27212],{"xmlns":1799},[1801,27213,27214,27230],{},[1804,27215,27216,27218,27220,27226,27228],{},[1807,27217,25224],{},[1811,27219,1813],{},[1815,27221,27222,27224],{},[1807,27223,8230],{},[1807,27225,1821],{},[1807,27227,2290],{},[1807,27229,8230],{},[1823,27231,27232],{"encoding":1825},"f=x^{T}Ax",[1788,27234,27236,27254],{"className":27235,"ariaHidden":1831},[1830],[1788,27237,27239,27242,27245,27248,27251],{"className":27238},[1835],[1788,27240],{"className":27241,"style":2041},[1839],[1788,27243,25224],{"className":27244,"style":25382},[1844,1845],[1788,27246],{"className":27247,"style":1851},[1850],[1788,27249,1813],{"className":27250},[1855],[1788,27252],{"className":27253,"style":1851},[1850],[1788,27255,27257,27260,27292,27295],{"className":27256},[1835],[1788,27258],{"className":27259,"style":1865},[1839],[1788,27261,27263,27266],{"className":27262},[1844],[1788,27264,8230],{"className":27265},[1844,1845],[1788,27267,27269],{"className":27268},[1875],[1788,27270,27272],{"className":27271},[1879],[1788,27273,27275],{"className":27274},[1883],[1788,27276,27278],{"className":27277,"style":1865},[1887],[1788,27279,27280,27283],{"style":1890},[1788,27281],{"className":27282,"style":1895},[1894],[1788,27284,27286],{"className":27285},[1899,1900,1901,1902],[1788,27287,27289],{"className":27288},[1844,1902],[1788,27290,1821],{"className":27291,"style":1909},[1844,1845,1902],[1788,27293,2290],{"className":27294},[1844,1845],[1788,27296,8230],{"className":27297},[1844,1845]," 正定 ",[1788,27300,27302,27315],{"className":27301},[1791],[1788,27303,27305],{"className":27304},[1795],[1797,27306,27307],{"xmlns":1799},[1801,27308,27309,27313],{},[1804,27310,27311],{},[1811,27312,22916],{},[1823,27314,22919],{"encoding":1825},[1788,27316,27318],{"className":27317,"ariaHidden":1831},[1830],[1788,27319,27321,27324],{"className":27320},[1835],[1788,27322],{"className":27323,"style":22929},[1839],[1788,27325,22916],{"className":27326},[1855]," 对任意 ",[1788,27329,27331,27349],{"className":27330},[1791],[1788,27332,27334],{"className":27333},[1795],[1797,27335,27336],{"xmlns":1799},[1801,27337,27338,27346],{},[1804,27339,27340,27342,27344],{},[1807,27341,8230],{},[1811,27343,1983],{"mathvariant":1982},[1985,27345,1987],{},[1823,27347,27348],{"encoding":1825},"x\\neq 0",[1788,27350,27352,27403],{"className":27351,"ariaHidden":1831},[1830],[1788,27353,27355,27358,27361,27364,27400],{"className":27354},[1835],[1788,27356],{"className":27357,"style":2041},[1839],[1788,27359,8230],{"className":27360},[1844,1845],[1788,27362],{"className":27363,"style":1851},[1850],[1788,27365,27367,27394,27397],{"className":27366},[1855],[1788,27368,27370],{"className":27369},[1855],[1788,27371,27373],{"className":27372},[1844,2029],[1788,27374,27376],{"className":27375},[2033],[1788,27377,27379,27382,27391],{"className":27378},[2037],[1788,27380],{"className":27381,"style":2041},[1839],[1788,27383,27385],{"className":27384},[2045],[1788,27386,27388],{"className":27387},[1844],[1788,27389,2052],{"className":27390},[1855],[1788,27392],{"className":27393},[2056],[1788,27395],{"className":27396},[1850,2060],[1788,27398,1813],{"className":27399},[1855],[1788,27401],{"className":27402,"style":1851},[1850],[1788,27404,27406,27409],{"className":27405},[1835],[1788,27407],{"className":27408,"style":4209},[1839],[1788,27410,1987],{"className":27411},[1844],[1788,27413,27415,27442],{"className":27414},[1791],[1788,27416,27418],{"className":27417},[1795],[1797,27419,27420],{"xmlns":1799},[1801,27421,27422,27439],{},[1804,27423,27424,27430,27432,27434,27437],{},[1815,27425,27426,27428],{},[1807,27427,8230],{},[1807,27429,1821],{},[1807,27431,2290],{},[1807,27433,8230],{},[1811,27435,27436],{},">",[1985,27438,1987],{},[1823,27440,27441],{"encoding":1825},"x^{T}Ax>0",[1788,27443,27445,27499],{"className":27444,"ariaHidden":1831},[1830],[1788,27446,27448,27452,27484,27487,27490,27493,27496],{"className":27447},[1835],[1788,27449],{"className":27450,"style":27451},[1839],"height:0.8804em;vertical-align:-0.0391em;",[1788,27453,27455,27458],{"className":27454},[1844],[1788,27456,8230],{"className":27457},[1844,1845],[1788,27459,27461],{"className":27460},[1875],[1788,27462,27464],{"className":27463},[1879],[1788,27465,27467],{"className":27466},[1883],[1788,27468,27470],{"className":27469,"style":1865},[1887],[1788,27471,27472,27475],{"style":1890},[1788,27473],{"className":27474,"style":1895},[1894],[1788,27476,27478],{"className":27477},[1899,1900,1901,1902],[1788,27479,27481],{"className":27480},[1844,1902],[1788,27482,1821],{"className":27483,"style":1909},[1844,1845,1902],[1788,27485,2290],{"className":27486},[1844,1845],[1788,27488,8230],{"className":27489},[1844,1845],[1788,27491],{"className":27492,"style":1851},[1850],[1788,27494,27436],{"className":27495},[1855],[1788,27497],{"className":27498,"style":1851},[1850],[1788,27500,27502,27505],{"className":27501},[1835],[1788,27503],{"className":27504,"style":4209},[1839],[1788,27506,1987],{"className":27507},[1844],"（定义）。",[1096,27510,6300,27511,11504,27539,27567,27568,27619,27620,27648,27649,9061,27677,27766,27767,11504,27795,10952,27846,8852,27874,27902],{},[1788,27512,27514,27527],{"className":27513},[1791],[1788,27515,27517],{"className":27516},[1795],[1797,27518,27519],{"xmlns":1799},[1801,27520,27521,27525],{},[1804,27522,27523],{},[1811,27524,22916],{},[1823,27526,22919],{"encoding":1825},[1788,27528,27530],{"className":27529,"ariaHidden":1831},[1830],[1788,27531,27533,27536],{"className":27532},[1835],[1788,27534],{"className":27535,"style":22929},[1839],[1788,27537,22916],{"className":27538},[1855],[1788,27540,27542,27555],{"className":27541},[1791],[1788,27543,27545],{"className":27544},[1795],[1797,27546,27547],{"xmlns":1799},[1801,27548,27549,27553],{},[1804,27550,27551],{},[1807,27552,25224],{},[1823,27554,25224],{"encoding":1825},[1788,27556,27558],{"className":27557,"ariaHidden":1831},[1830],[1788,27559,27561,27564],{"className":27560},[1835],[1788,27562],{"className":27563,"style":2041},[1839],[1788,27565,25224],{"className":27566,"style":25382},[1844,1845]," 的正惯性指数 ",[1788,27569,27571,27589],{"className":27570},[1791],[1788,27572,27574],{"className":27573},[1795],[1797,27575,27576],{"xmlns":1799},[1801,27577,27578,27586],{},[1804,27579,27580,27582,27584],{},[1807,27581,1096],{},[1811,27583,1813],{},[1807,27585,2301],{},[1823,27587,27588],{"encoding":1825},"p=n",[1788,27590,27592,27610],{"className":27591,"ariaHidden":1831},[1830],[1788,27593,27595,27598,27601,27604,27607],{"className":27594},[1835],[1788,27596],{"className":27597,"style":5356},[1839],[1788,27599,1096],{"className":27600},[1844,1845],[1788,27602],{"className":27603,"style":1851},[1850],[1788,27605,1813],{"className":27606},[1855],[1788,27608],{"className":27609,"style":1851},[1850],[1788,27611,27613,27616],{"className":27612},[1835],[1788,27614],{"className":27615,"style":3114},[1839],[1788,27617,2301],{"className":27618},[1844,1845],"；\n② ",[1788,27621,27623,27636],{"className":27622},[1791],[1788,27624,27626],{"className":27625},[1795],[1797,27627,27628],{"xmlns":1799},[1801,27629,27630,27634],{},[1804,27631,27632],{},[1811,27633,22916],{},[1823,27635,22919],{"encoding":1825},[1788,27637,27639],{"className":27638,"ariaHidden":1831},[1830],[1788,27640,27642,27645],{"className":27641},[1835],[1788,27643],{"className":27644,"style":22929},[1839],[1788,27646,22916],{"className":27647},[1855]," 存在可逆矩阵 ",[1788,27650,27652,27665],{"className":27651},[1791],[1788,27653,27655],{"className":27654},[1795],[1797,27656,27657],{"xmlns":1799},[1801,27658,27659,27663],{},[1804,27660,27661],{},[1807,27662,1809],{},[1823,27664,1809],{"encoding":1825},[1788,27666,27668],{"className":27667,"ariaHidden":1831},[1830],[1788,27669,27671,27674],{"className":27670},[1835],[1788,27672],{"className":27673,"style":1840},[1839],[1788,27675,1809],{"className":27676,"style":1846},[1844,1845],[1788,27678,27680,27704],{"className":27679},[1791],[1788,27681,27683],{"className":27682},[1795],[1797,27684,27685],{"xmlns":1799},[1801,27686,27687,27701],{},[1804,27688,27689,27691,27693,27699],{},[1807,27690,2290],{},[1811,27692,1813],{},[1815,27694,27695,27697],{},[1807,27696,1809],{},[1807,27698,1821],{},[1807,27700,1809],{},[1823,27702,27703],{"encoding":1825},"A=D^{T}D",[1788,27705,27707,27725],{"className":27706,"ariaHidden":1831},[1830],[1788,27708,27710,27713,27716,27719,27722],{"className":27709},[1835],[1788,27711],{"className":27712,"style":1840},[1839],[1788,27714,2290],{"className":27715},[1844,1845],[1788,27717],{"className":27718,"style":1851},[1850],[1788,27720,1813],{"className":27721},[1855],[1788,27723],{"className":27724,"style":1851},[1850],[1788,27726,27728,27731,27763],{"className":27727},[1835],[1788,27729],{"className":27730,"style":1865},[1839],[1788,27732,27734,27737],{"className":27733},[1844],[1788,27735,1809],{"className":27736,"style":1846},[1844,1845],[1788,27738,27740],{"className":27739},[1875],[1788,27741,27743],{"className":27742},[1879],[1788,27744,27746],{"className":27745},[1883],[1788,27747,27749],{"className":27748,"style":1865},[1887],[1788,27750,27751,27754],{"style":1890},[1788,27752],{"className":27753,"style":1895},[1894],[1788,27755,27757],{"className":27756},[1899,1900,1901,1902],[1788,27758,27760],{"className":27759},[1844,1902],[1788,27761,1821],{"className":27762,"style":1909},[1844,1845,1902],[1788,27764,1809],{"className":27765,"style":1846},[1844,1845],"；\n③ ",[1788,27768,27770,27783],{"className":27769},[1791],[1788,27771,27773],{"className":27772},[1795],[1797,27774,27775],{"xmlns":1799},[1801,27776,27777,27781],{},[1804,27778,27779],{},[1811,27780,22916],{},[1823,27782,22919],{"encoding":1825},[1788,27784,27786],{"className":27785,"ariaHidden":1831},[1830],[1788,27787,27789,27792],{"className":27788},[1835],[1788,27790],{"className":27791,"style":22929},[1839],[1788,27793,22916],{"className":27794},[1855],[1788,27796,27798,27816],{"className":27797},[1791],[1788,27799,27801],{"className":27800},[1795],[1797,27802,27803],{"xmlns":1799},[1801,27804,27805,27813],{},[1804,27806,27807,27809,27811],{},[1807,27808,2290],{},[1811,27810,26448],{},[1807,27812,3192],{},[1823,27814,27815],{"encoding":1825},"A\\cong E",[1788,27817,27819,27837],{"className":27818,"ariaHidden":1831},[1830],[1788,27820,27822,27825,27828,27831,27834],{"className":27821},[1835],[1788,27823],{"className":27824,"style":1840},[1839],[1788,27826,2290],{"className":27827},[1844,1845],[1788,27829],{"className":27830,"style":1851},[1850],[1788,27832,26448],{"className":27833},[1855],[1788,27835],{"className":27836,"style":1851},[1850],[1788,27838,27840,27843],{"className":27839},[1835],[1788,27841],{"className":27842,"style":1840},[1839],[1788,27844,3192],{"className":27845,"style":3222},[1844,1845],[1788,27847,27849,27862],{"className":27848},[1791],[1788,27850,27852],{"className":27851},[1795],[1797,27853,27854],{"xmlns":1799},[1801,27855,27856,27860],{},[1804,27857,27858],{},[1807,27859,2290],{},[1823,27861,2290],{"encoding":1825},[1788,27863,27865],{"className":27864,"ariaHidden":1831},[1830],[1788,27866,27868,27871],{"className":27867},[1835],[1788,27869],{"className":27870,"style":1840},[1839],[1788,27872,2290],{"className":27873},[1844,1845],[1788,27875,27877,27890],{"className":27876},[1791],[1788,27878,27880],{"className":27879},[1795],[1797,27881,27882],{"xmlns":1799},[1801,27883,27884,27888],{},[1804,27885,27886],{},[1807,27887,3192],{},[1823,27889,3192],{"encoding":1825},[1788,27891,27893],{"className":27892,"ariaHidden":1831},[1830],[1788,27894,27896,27899],{"className":27895},[1835],[1788,27897],{"className":27898,"style":1840},[1839],[1788,27900,3192],{"className":27901,"style":3222},[1844,1845]," 合同。",[1096,27904,27905],{},"②③④的推导：",[1096,27907,27908],{},[2114,27909],{"alt":27910,"src":27911},"正定条件推导","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be29ead4d.png",[1096,27913,6724,27914,11504,27942,27970,27971,28063,28064,11504,28092,28120,28121,2389],{},[1788,27915,27917,27930],{"className":27916},[1791],[1788,27918,27920],{"className":27919},[1795],[1797,27921,27922],{"xmlns":1799},[1801,27923,27924,27928],{},[1804,27925,27926],{},[1811,27927,22916],{},[1823,27929,22919],{"encoding":1825},[1788,27931,27933],{"className":27932,"ariaHidden":1831},[1830],[1788,27934,27936,27939],{"className":27935},[1835],[1788,27937],{"className":27938,"style":22929},[1839],[1788,27940,22916],{"className":27941},[1855],[1788,27943,27945,27958],{"className":27944},[1791],[1788,27946,27948],{"className":27947},[1795],[1797,27949,27950],{"xmlns":1799},[1801,27951,27952,27956],{},[1804,27953,27954],{},[1807,27955,2290],{},[1823,27957,2290],{"encoding":1825},[1788,27959,27961],{"className":27960,"ariaHidden":1831},[1830],[1788,27962,27964,27967],{"className":27963},[1835],[1788,27965],{"className":27966,"style":1840},[1839],[1788,27968,2290],{"className":27969},[1844,1845]," 的特征值 ",[1788,27972,27974,27996],{"className":27973},[1791],[1788,27975,27977],{"className":27976},[1795],[1797,27978,27979],{"xmlns":1799},[1801,27980,27981,27993],{},[1804,27982,27983,27989,27991],{},[2881,27984,27985,27987],{},[1807,27986,20664],{},[1807,27988,4034],{},[1811,27990,27436],{},[1985,27992,1987],{},[1823,27994,27995],{"encoding":1825},"\\lambda_i>0",[1788,27997,27999,28054],{"className":27998,"ariaHidden":1831},[1830],[1788,28000,28002,28005,28045,28048,28051],{"className":28001},[1835],[1788,28003],{"className":28004,"style":17730},[1839],[1788,28006,28008,28011],{"className":28007},[1844],[1788,28009,20664],{"className":28010},[1844,1845],[1788,28012,28014],{"className":28013},[1875],[1788,28015,28017,28037],{"className":28016},[1879,2931],[1788,28018,28020,28034],{"className":28019},[1883],[1788,28021,28023],{"className":28022,"style":4069},[1887],[1788,28024,28025,28028],{"style":4072},[1788,28026],{"className":28027,"style":1895},[1894],[1788,28029,28031],{"className":28030},[1899,1900,1901,1902],[1788,28032,4034],{"className":28033},[1844,1845,1902],[1788,28035,2958],{"className":28036},[2957],[1788,28038,28040],{"className":28039},[1883],[1788,28041,28043],{"className":28042,"style":2965},[1887],[1788,28044],{},[1788,28046],{"className":28047,"style":1851},[1850],[1788,28049,27436],{"className":28050},[1855],[1788,28052],{"className":28053,"style":1851},[1850],[1788,28055,28057,28060],{"className":28056},[1835],[1788,28058],{"className":28059,"style":4209},[1839],[1788,28061,1987],{"className":28062},[1844],"；\n⑤ ",[1788,28065,28067,28080],{"className":28066},[1791],[1788,28068,28070],{"className":28069},[1795],[1797,28071,28072],{"xmlns":1799},[1801,28073,28074,28078],{},[1804,28075,28076],{},[1811,28077,22916],{},[1823,28079,22919],{"encoding":1825},[1788,28081,28083],{"className":28082,"ariaHidden":1831},[1830],[1788,28084,28086,28089],{"className":28085},[1835],[1788,28087],{"className":28088,"style":22929},[1839],[1788,28090,22916],{"className":28091},[1855],[1788,28093,28095,28108],{"className":28094},[1791],[1788,28096,28098],{"className":28097},[1795],[1797,28099,28100],{"xmlns":1799},[1801,28101,28102,28106],{},[1804,28103,28104],{},[1807,28105,2290],{},[1823,28107,2290],{"encoding":1825},[1788,28109,28111],{"className":28110,"ariaHidden":1831},[1830],[1788,28112,28114,28117],{"className":28113},[1835],[1788,28115],{"className":28116,"style":1840},[1839],[1788,28118,2290],{"className":28119},[1844,1845]," 的全部顺序主子式 ",[1788,28122,28124,28140],{"className":28123},[1791],[1788,28125,28127],{"className":28126},[1795],[1797,28128,28129],{"xmlns":1799},[1801,28130,28131,28137],{},[1804,28132,28133,28135],{},[1811,28134,27436],{},[1985,28136,1987],{},[1823,28138,28139],{"encoding":1825},">0",[1788,28141,28143,28155],{"className":28142,"ariaHidden":1831},[1830],[1788,28144,28146,28149,28152],{"className":28145},[1835],[1788,28147],{"className":28148,"style":15149},[1839],[1788,28150,27436],{"className":28151},[1855],[1788,28153],{"className":28154,"style":1851},[1850],[1788,28156,28158,28161],{"className":28157},[1835],[1788,28159],{"className":28160,"style":4209},[1839],[1788,28162,1987],{"className":28163},[1844],[1912,28165,28166,28171],{},[1096,28167,28168],{},[1099,28169,28170],{},"二次型正定的必要条件：",[1096,28172,6300,28173,28273,28274,27619,28302,2389],{},[1788,28174,28176,28202],{"className":28175},[1791],[1788,28177,28179],{"className":28178},[1795],[1797,28180,28181],{"xmlns":1799},[1801,28182,28183,28199],{},[1804,28184,28185,28195,28197],{},[2881,28186,28187,28189],{},[1807,28188,1105],{},[1804,28190,28191,28193],{},[1807,28192,4034],{},[1807,28194,4034],{},[1811,28196,27436],{},[1985,28198,1987],{},[1823,28200,28201],{"encoding":1825},"a_{ii}>0",[1788,28203,28205,28264],{"className":28204,"ariaHidden":1831},[1830],[1788,28206,28208,28212,28255,28258,28261],{"className":28207},[1835],[1788,28209],{"className":28210,"style":28211},[1839],"height:0.6891em;vertical-align:-0.15em;",[1788,28213,28215,28218],{"className":28214},[1844],[1788,28216,1105],{"className":28217},[1844,1845],[1788,28219,28221],{"className":28220},[1875],[1788,28222,28224,28247],{"className":28223},[1879,2931],[1788,28225,28227,28244],{"className":28226},[1883],[1788,28228,28230],{"className":28229,"style":4069},[1887],[1788,28231,28232,28235],{"style":4072},[1788,28233],{"className":28234,"style":1895},[1894],[1788,28236,28238],{"className":28237},[1899,1900,1901,1902],[1788,28239,28241],{"className":28240},[1844,1902],[1788,28242,20407],{"className":28243},[1844,1845,1902],[1788,28245,2958],{"className":28246},[2957],[1788,28248,28250],{"className":28249},[1883],[1788,28251,28253],{"className":28252,"style":2965},[1887],[1788,28254],{},[1788,28256],{"className":28257,"style":1851},[1850],[1788,28259,27436],{"className":28260},[1855],[1788,28262],{"className":28263,"style":1851},[1850],[1788,28265,28267,28270],{"className":28266},[1835],[1788,28268],{"className":28269,"style":4209},[1839],[1788,28271,1987],{"className":28272},[1844],"，对角线元素全部大于 ",[1788,28275,28277,28290],{"className":28276},[1791],[1788,28278,28280],{"className":28279},[1795],[1797,28281,28282],{"xmlns":1799},[1801,28283,28284,28288],{},[1804,28285,28286],{},[1985,28287,1987],{},[1823,28289,1987],{"encoding":1825},[1788,28291,28293],{"className":28292,"ariaHidden":1831},[1830],[1788,28294,28296,28299],{"className":28295},[1835],[1788,28297],{"className":28298,"style":4209},[1839],[1788,28300,1987],{"className":28301},[1844],[1788,28303,28305,28327],{"className":28304},[1791],[1788,28306,28308],{"className":28307},[1795],[1797,28309,28310],{"xmlns":1799},[1801,28311,28312,28324],{},[1804,28313,28314,28316,28318,28320,28322],{},[1807,28315,2285],{"mathvariant":1982},[1807,28317,2290],{},[1807,28319,2285],{"mathvariant":1982},[1811,28321,27436],{},[1985,28323,1987],{},[1823,28325,28326],{"encoding":1825},"|A|>0",[1788,28328,28330,28354],{"className":28329,"ariaHidden":1831},[1830],[1788,28331,28333,28336,28339,28342,28345,28348,28351],{"className":28332},[1835],[1788,28334],{"className":28335,"style":2003},[1839],[1788,28337,2285],{"className":28338},[1844],[1788,28340,2290],{"className":28341},[1844,1845],[1788,28343,2285],{"className":28344},[1844],[1788,28346],{"className":28347,"style":1851},[1850],[1788,28349,27436],{"className":28350},[1855],[1788,28352],{"className":28353,"style":1851},[1850],[1788,28355,28357,28360],{"className":28356},[1835],[1788,28358],{"className":28359,"style":4209},[1839],[1788,28361,1987],{"className":28362},[1844],[1096,28364,28365],{},"最好是使用充要条件 ①④⑤ 判断二次型是否正定。如果非要用定义法，来看个例题：",[1096,28367,28368],{},[2114,28369],{"alt":28370,"src":28371},"正定例题（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2b97057.png",[1096,28373,28374,28375,28403],{},"注意上题，不能直接将 ",[1788,28376,28378,28391],{"className":28377},[1791],[1788,28379,28381],{"className":28380},[1795],[1797,28382,28383],{"xmlns":1799},[1801,28384,28385,28389],{},[1804,28386,28387],{},[1807,28388,25224],{},[1823,28390,25224],{"encoding":1825},[1788,28392,28394],{"className":28393,"ariaHidden":1831},[1830],[1788,28395,28397,28400],{"className":28396},[1835],[1788,28398],{"className":28399,"style":2041},[1839],[1788,28401,25224],{"className":28402,"style":25382},[1844,1845]," 判定为正定：",[1096,28405,28406,28407,2389],{},"因为将二次型化为标准型的过程一定要做",[1099,28408,26547],{},[1096,28410,28411],{},[2114,28412],{"alt":28413,"src":28414},"可逆线性变换之注","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2b73fd4.png",[1096,28416,28417],{},[1099,28418,21255],{},[1096,28420,28421],{},[2114,28422],{"alt":28423,"src":28424},"正定例题1（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2bde67d.png",[1096,28426,28427],{},[2114,28428],{"alt":28429,"src":28430},"正定例题1（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2bbdd65.jpeg",[1096,28432,28433],{},[1099,28434,21266],{},[1096,28436,28437],{},[2114,28438],{"alt":28439,"src":28440},"正定例题2（一）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2c370ad.png",[1096,28442,28443],{},[2114,28444],{"alt":28445,"src":28446},"正定例题2（二）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2bd06ac.png",[1096,28448,28449],{},[2114,28450],{"alt":28451,"src":28452},"正定例题2（三）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2de5d54.png",[1096,28454,28455],{},[2114,28456],{"alt":28457,"src":28458},"正定例题2（四）","https:\u002F\u002Ffree-img.400040.xyz\u002F4\u002F2024\u002F07\u002F31\u002F66a9be2f0a59c.png",{"title":28460,"searchDepth":28461,"depth":28461,"links":28462},"",4,[28463,28471,28486,28490,28499,28500,28501,28507,28508,28513,28514,28515,28516],{"id":1093,"depth":28464,"text":1094,"children":28465},2,[28466,28467,28468,28469,28470],{"id":1206,"depth":28461,"text":1207},{"id":1305,"depth":28461,"text":1306},{"id":1396,"depth":28461,"text":1397},{"id":1532,"depth":28461,"text":1533},{"id":1689,"depth":28461,"text":1690},{"id":1777,"depth":28464,"text":1778,"children":28472},[28473,28475,28476,28477,28479,28480,28481,28482,28483,28485],{"id":1782,"depth":28474,"text":1783},3,{"id":2155,"depth":28474,"text":2156},{"id":2392,"depth":28474,"text":2393},{"id":2405,"depth":28474,"text":28478},"4. 判定解的情况，单纯求 r(A), r(A,b)r(A),\\,r(A,b)r(A),r(A,b) 的过程行列变换都可",{"id":2831,"depth":28474,"text":2832},{"id":3128,"depth":28474,"text":3129},{"id":3144,"depth":28474,"text":3145},{"id":3157,"depth":28474,"text":3158},{"id":3170,"depth":28474,"text":28484},"9. 求逆矩阵时，对 (A,E)(A,E)(A,E) 仅做初等行变换",{"id":2823,"depth":28474,"text":2823},{"id":3802,"depth":28464,"text":3803,"children":28487},[28488,28489],{"id":3936,"depth":28474,"text":3937},{"id":3966,"depth":28474,"text":3967},{"id":3976,"depth":28464,"text":3977,"children":28491},[28492,28493,28494,28496,28498],{"id":3980,"depth":28474,"text":3981},{"id":4374,"depth":28474,"text":4375},{"id":4710,"depth":28474,"text":28495},"3. kkk 阶子式",{"id":5218,"depth":28474,"text":28497},"4. kkk 阶主子式",{"id":6060,"depth":28474,"text":6061},{"id":6296,"depth":28464,"text":6297},{"id":8354,"depth":28464,"text":8355},{"id":8402,"depth":28464,"text":8403,"children":28502},[28503,28504,28505,28506],{"id":8817,"depth":28474,"text":8818},{"id":9125,"depth":28474,"text":9126},{"id":12165,"depth":28474,"text":12166},{"id":14059,"depth":28474,"text":14060},{"id":14999,"depth":28464,"text":15000},{"id":20102,"depth":28464,"text":20103,"children":28509},[28510,28511,28512],{"id":20106,"depth":28474,"text":20107},{"id":20421,"depth":28474,"text":20422},{"id":21243,"depth":28474,"text":21244},{"id":21275,"depth":28464,"text":21276},{"id":26177,"depth":28464,"text":26178},{"id":26600,"depth":28464,"text":26601},{"id":27164,"depth":28464,"text":27165},"https:\u002F\u002Fpic3.zhimg.com\u002Fv2-2d64b070c08f997649778c339779bdfe_b.jpeg","收集到的一些高代资料","md",true,{"uuid":28522,"slots":28523},"093d879a-1054-11f0-9848-0b39a1ee406d",{},20,{"title":1085,"description":28518},"posts\u002F2024\u002F2024-07-26-线性代数与空间解析几何知识点全汇总",1,[49,50,51],"qgsNPg3DyC7fDHbeFIxhLxevjWcNtkLtD1EJ9MCITaY",1790443289717]