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深度之眼(七)——矩阵的初等变换(附:数模一些模型的解释)
2022-07-07 13:32:00 【光追雨】
文章目录
一、初等变换的引入
高斯消元法
二、三种矩阵的初等变换以及对应的三种初等矩阵,矩阵的标准
2.1 三种矩阵的初等变换
2.2 例
2.3 矩阵的标准型
2.4 三种初等矩阵
第一个是第i行和第j行交换
第二个是第i行乘以k倍
第三个是第j行乘以k倍加到第i行上
下方的左边Q1到Qj是初等行变换,Qj到Qi是初等列变换
三、初等变换的常用性质与矩阵逆矩阵的另外一种简单求法
3.1 常用性质
3.2 矩阵逆的简单求法
可逆的矩阵一定可以通过初等行变换变成单位矩阵
四、矩阵秩的定义以及性质
算秩的时候,尽量构成下三角矩阵
五、线性方程组解的个数
六、矩阵的秩在机器学习线性回归算法中的运用(中级)
博主在看到a = (xTx)-1xTY的时候,忽然想起来,我曾经在给大一讲课时候的一个教案
这个:4-1预测与回归
很相像,可以联想学习下
N < n的情况得下次讲
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