第一章行列式 4§1.1二阶与三阶行列式..........................................................................................4一、二阶行列式.................................................................................................4二、三阶行列式.................................................................................................6§1.2 阶行列式..................................................................................................7一、排列及逆序数..............................................................................................7二、阶行列式.................................................................................................8§1.3行列式的性质...............................................................................................11§1.4行列式按行（列）展开.................................................................................16§1.5克拉默法则....................................................................................................23习题1.....................................................................................................................27第二章矩阵及其运算 31§2.1矩阵的概念...................................................................................................31一、矩阵的定义...............................................................................................31二、几种特殊的矩阵........................................................................................34三、线性变换...................................................................................................36§2.2矩阵的运算...................................................................................................37一、矩阵的加法...............................................................................................37二、数与矩阵的乘法........................................................................................38三、矩阵的乘法...............................................................................................39四、矩阵的转置...............................................................................................42五、方阵的幂...................................................................................................44六、方阵的行列式............................................................................................45七、伴随矩阵...................................................................................................46八、对称矩阵...................................................................................................48§2.3逆矩阵..........................................................................................................49一、逆矩阵的概念............................................................................................49二、矩阵可逆的充要条件.................................................................................50三、矩阵方程和矩阵多项式..............................................................................52§2.4分块矩阵......................................................................................................55一、分块矩阵的概念........................................................................................55二、分块矩阵的运算........................................................................................56§2.5矩阵的初等变换............................................................................................61一、矩阵的初等变换........................................................................................61二、初等矩阵...................................................................................................64三、初等变换法求逆矩阵.................................................................................66四、初等变换法求解矩阵方程..........................................................................69§2.6矩阵的秩......................................................................................................70一、矩阵秩的概念............................................................................................71二、矩阵秩的性质............................................................................................72三、矩阵秩的求法............................................................................................73习题2.....................................................................................................................76第三章 线性方程组与向量...........82§3.1线性方程组有解的判别法..............................................................................82一、非齐次线性方程组.....................................................................................82二、齐次线性方程组........................................................................................88§3.2向量及其线性运算.........................................................................................90一、向量的概念...............................................................................................90二、向量的线性运算........................................................................................91§3.3向量组的线性相关性......................................................................................92一、向量组的线性组合.....................................................................................92二、向量组的线性相关性.................................................................................95§3.4向量组的秩....................................................................................................99一、向量组的等价............................................................................................99二、向量组的极大无关组和秩.........................................................................102三、矩阵的秩与向量组的秩的关系..................................................................103§3.5向量空间......................................................................................................105一、向量空间的概念.......................................................................................105二、向量空间的基..........................................................................................107§3.6线性方程组解的结构...................................................................................111一、齐次线性方程组解的结构.........................................................................111二、非齐次线性方程组解的结构.....................................................................116习题3....................................................................................................................120第四章矩阵的特征值及二次型...126§4.1向量的内积、长度及正交性.........................................................................126一、向量的内积..............................................................................................126二、向量的长度..............................................................................................127三、正交向量组..............................................................................................128四、标准正交基..............................................................................................130五、正交矩阵与正交变换................................................................................133§4.2方阵的特征值与特征向量.............................................................................134一、特征值与特征向量...................................................................................134二、特征值与特征向量的性质.........................................................................138§4.3相似矩阵.....................................................................................................142一、相似矩阵的概念.......................................................................................142二、方阵的相似对角化...................................................................................144§4.4实对称矩阵的对角化....................................................................................147一、实对称矩阵的特征值与特征向量..............................................................147二、实对称矩阵的正交相似对角化..................................................................148§4.5二次型.........................................................................................................152一、二次型的概念..........................................................................................152二、二次型的矩阵形式...................................................................................153§4.6二次型的标准型...........................................................................................155一、正交变换法化二次型为标准型..................................................................155二、配方法化二次型为标准型.........................................................................159§4.7正定二次型.................................................................................................163一、正定二次型的概念...................................................................................163二、赫尔维茨定理..........................................................................................165习题4....................................................................................................................167习题答案 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