2024年3月17日发(作者：高三数学试卷函数题)
目 录
第 1 章 行列式 ·························· 1
§1.1 二阶与三阶行列式 ····················· 1
§1.2 排列及其逆序数 ······················ 3
§1.3 n 阶行列式的定义 ····················· 4
§1.4 对换 ··························· 6
§1.5 行列式的性质 ······················· 8
§1.6 行列式按行(列)展开 ···················· 14
§1.7 Matlab 在行列式计算中的应用 ················ 22
习题 1 ······················································································· 22
第 2 章 矩阵 ··························· 26
§2.1 矩阵的概念 ························ 26
§2.2 矩阵的关系和运算 ····················· 31
§2.3 伴随矩阵和逆矩阵 ····················· 39
§2.4 矩阵的分块法 ······················· 45
§2.5 矩阵的初等变换和初等矩阵 ················· 52
§2.6 矩阵的秩 ························· 59
§2.7 Matlab 在矩阵运算与初等变换中的应用 ············ 63
习题 2 ······················································································· 66
第 3 章 线性方程组 ························ 72
§3.1 Cramer 法则 ······················· 72
§3.2 一般线性方程组的解 ···················· 74
§3.3 Matlab 在解线性方程组中的应用 ··············· 85
习题 3 ······················································································· 86
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高 等 代 数
第 4 章 向量组的线性相关性 ···················· 89
§4.1 向量组及其线性组合 ···················· 89
§4.2 向量组的线性相关性 ···················· 92
§4.3 向量组的秩 ························ 97
§4.4 线性方程组解的结构 ··················· 100
§4.5 Matlab 在向量组线性相关性中的应用 ············ 106
习题 4 ······················································································ 107
第 5 章 线性空间与线性变换 ··················· 111
§5.1 数环、数域与映射 ···················· 111
§5.2 线性空间及其性质 ···················· 115
§5.3 基、维数与坐标 ····················· 118
§5.4 基变换与坐标变换 ···················· 120
§5.5 线性变换 ························ 123
§5.6 线性变换的矩阵表示 ··················· 127
§5.7 欧氏空间 ························ 132
§5.8 Matlab 在线性空间和线性变换中的应用 ··········· 141
习题 5 ······················································································ 144
第 6 章 相似矩阵及二次型 ···················· 150
§6.1 方阵的特征值与特征向量 ················· 150
§6.2 相似矩阵 ························ 155
§6.3 实对称矩阵的相似矩阵 ·················· 158
§6.4 二次型及其标准形 ···················· 161
§6.5 化二次型为标准形 ···················· 163
§6.6 正定二次型 ······················· 169
§6.7 Matlab 在相似矩阵和二次型中的应用 ············ 172
习题 6 ······················································································ 175
第 7 章 多项式 ························· 179
§7.1 一元多项式的定义和运算 ················· 179
§7.2 多项式的整除性 ····················· 182
§7.3 多项式的最大公因式和互素 ················ 186
§7.4 多项式的分解 ······················ 191
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矩阵,线性,行列式,变换
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