线性代数-----矩阵复习2
1.逆矩阵
对于n阶方阵A，如果存在n阶方阵B，使得
AB=BA=E，
那么矩阵A称为可逆的，而B称为A的逆矩阵.
（1）如果矩阵A可逆，则A的逆矩阵是唯一的
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2.
n阶矩阵A为可逆的充分必要条件是|A|不等于0，而且A逆= （1/|A|） A*, 其中A*为方阵A的伴随矩阵。
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3.
对于n阶矩阵A，若行列式|A|不等于0，则A是满秩的。
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4.可逆矩阵的性质
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5.分块矩阵
用若干条横线和纵线把矩阵A分成若干小块，每一个小
块作为一个矩阵，称为A的子块(或子矩阵). 把A的每一个子
块作为一个元素构成的矩阵称为分块矩阵.
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6.伴随矩阵
（1）伴随矩阵定义：
（2）二阶伴随矩阵：主对调，副取反。具体来说就是主对角线元素(a11和a22)交换位置，副对角线上的元素(a12和a21)取其相反数。
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7.矩阵的初等变换
对矩阵施以下列三种变换之一，称为初等变换.
(1)交换矩阵的某两行(列)；
(2)以数k不等于0乘矩阵的某一行(列)；
(3)把矩阵的某一行(列)的k倍加到另一行(列)上.
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8.行阶梯型矩阵和行最简形矩阵
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9.对单位矩阵E施以一次初等变换得到的矩阵称为初等矩阵（或初等方阵）
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