目 錄
第 1 章 行列式 .............................................................................................. 1
1.1 二階、三階行列式 ................................................................................................ 1
1.2 n階行列式 .............................................................................................................. 3
1.3 行列式的性質 ........................................................................................................ 7
1.4 行列式按行（列）展開 ...................................................................................... 10
1.5 克拉默法則 .......................................................................................................... 15
習題1 ............................................................................................................................. 18
自測題一 ....................................................................................................................... 21
第 2 章 矩陣 ................................................................................................ 24
2.1 矩陣的概念 .......................................................................................................... 24
2.2 矩陣的運算 .......................................................................................................... 27
2.3 可逆矩陣 .............................................................................................................. 35
2.4 矩陣的分塊 .......................................................................................................... 38
2.5 矩陣的初等變換 .................................................................................................. 44
2.6 矩陣的秩 .............................................................................................................. 50
習題2 ............................................................................................................................. 53
自測題二 ....................................................................................................................... 56
第 3 章 線性方程組的消元法 ...................................................................... 59
3.1 線性方程組的消元法 .......................................................................................... 59
3.2 線性方程組解的判斷 .......................................................................................... 63
習題3 ............................................................................................................................. 68
自測題三 ....................................................................................................................... 68
第 4 章 向量及向量間的線性關系 ............................................................. 71
4.1 n維向量及其線性運算 ........................................................................................ 71
4.2 向量間的線性關系 .............................................................................................. 74
4.3 向量組的秩 .......................................................................................................... 80
4.4 線性方程組解的結構 .......................................................................................... 86
習題4 ............................................................................................................................. 94
自測題四 ....................................................................................................................... 96
第 5 章 矩陣的特征值和特征向量 ............................................................. 100
5.1 矩陣的特征值和特征向量 ................................................................................ 100
5.2 相似矩陣 ............................................................................................................ 106
5.3 實向量的內積與正交矩陣 ................................................................................ 113
5.4 實對稱矩陣的對角化 ........................................................................................ 119
習題5 ........................................................................................................................... 125
自測題五 ..................................................................................................................... 127
第 6 章 二次型 .......................................................................................... 130
6.1 二次型的基本概念 ............................................................................................ 130
6.2 二次型的標準形與規(guī)范形 ................................................................................ 134
6.3 二次型和對稱矩陣的正定性 ............................................................................ 140
習題6 ........................................................................................................................... 144
自測題六 ..................................................................................................................... 145