README.md · CC/math

[![MIT Licence](https://badges.frapsoft.com/os/mit/mit.svg?v=103)](https://opensource.org/licenses/mit-license.php)

# 中文 Linear Algebra （线性代数） 笔记

## Overview （概述）

Most of the content comes from the web.<br>
大部分内容来自网络。

I know my knowledge of linear algebra is not very thorough, so I re-learn linear algebra, record the corresponding notes.<br>
由于我们对线性代数的知识了解不深，特意重新学习一次线代，记录下相应笔记。

课程顺序是按照麻省理工公开课的 [Linear Algebra](http://open.163.com/special/opencourse/daishu.html) 记录的学习笔记。

----

## Contents （目录）

---

- [01. **方程组的几何解释**](https://github.com/chenyyx/notes-linear-algebra/tree/master/01-%E6%96%B9%E7%A8%8B%E7%BB%84%E7%9A%84%E5%87%A0%E4%BD%95%E8%A7%A3%E9%87%8A)
	 - [01.01 方程组的几何解释](https://github.com/chenyyx/notes-linear-algebra/blob/master/01-%E6%96%B9%E7%A8%8B%E7%BB%84%E7%9A%84%E5%87%A0%E4%BD%95%E8%A7%A3%E9%87%8A/01-%E6%96%B9%E7%A8%8B%E7%BB%84%E7%9A%84%E5%87%A0%E4%BD%95%E8%A7%A3%E9%87%8A.md)
- [02. **矩阵消元**](02-python-essentials)
	 - [02.01 矩阵消元](https://github.com/chenyyx/notes-linear-algebra/blob/master/02-%E7%9F%A9%E9%98%B5%E6%B6%88%E5%85%83/02-%E7%9F%A9%E9%98%B5%E6%B6%88%E5%85%83.md)
- [03. **乘法和逆矩阵**](https://github.com/chenyyx/notes-linear-algebra/tree/master/03-%E4%B9%98%E6%B3%95%E5%92%8C%E9%80%86%E7%9F%A9%E9%98%B5)
	 - [03.01 矩阵乘法和逆矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/03-%E4%B9%98%E6%B3%95%E5%92%8C%E9%80%86%E7%9F%A9%E9%98%B5/03-%E4%B9%98%E6%B3%95%E5%92%8C%E9%80%86%E7%9F%A9%E9%98%B5.md)
- [04. **A的LU分解**](https://github.com/chenyyx/notes-linear-algebra/tree/master/04-A%E7%9A%84LU%E5%88%86%E8%A7%A3)
	 - [04.01 A的LU分解](https://github.com/chenyyx/notes-linear-algebra/blob/master/04-A%E7%9A%84LU%E5%88%86%E8%A7%A3/04-A%E7%9A%84LU%E5%88%86%E8%A7%A3.md)
- [05. **转置-置换-向量空间R**](https://github.com/chenyyx/notes-linear-algebra/tree/master/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R)
	 - [05.01 矩阵转置](https://github.com/chenyyx/notes-linear-algebra/blob/master/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R.md)
	 - [05.02 置换](https://github.com/chenyyx/notes-linear-algebra/blob/master/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R.md)
	 - [05.03 向量空间 R](https://github.com/chenyyx/notes-linear-algebra/blob/master/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R/05-%E8%BD%AC%E7%BD%AE-%E7%BD%AE%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4R.md)
- [06. **列空间和零空间**](https://github.com/chenyyx/notes-linear-algebra/tree/master/06-%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4)
	 - [06.01 列空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/06-%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4/06-%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4.md)
	 - [06.02 零空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/06-%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4/06-%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4.md)
- [07. **求解Ax=0:主变量,特解**](https://github.com/chenyyx/notes-linear-algebra/tree/master/07-%E6%B1%82%E8%A7%A3Ax%3D0-%E4%B8%BB%E5%8F%98%E9%87%8F-%E7%89%B9%E8%A7%A3)
	 - [07.01 主变量](https://github.com/chenyyx/notes-linear-algebra/blob/master/07-%E6%B1%82%E8%A7%A3Ax%3D0-%E4%B8%BB%E5%8F%98%E9%87%8F-%E7%89%B9%E8%A7%A3/07-%E6%B1%82%E8%A7%A3Ax%3D0-%E4%B8%BB%E5%8F%98%E9%87%8F-%E7%89%B9%E8%A7%A3.md)
	 - [07.02 特解](https://github.com/chenyyx/notes-linear-algebra/blob/master/07-%E6%B1%82%E8%A7%A3Ax%3D0-%E4%B8%BB%E5%8F%98%E9%87%8F-%E7%89%B9%E8%A7%A3/07-%E6%B1%82%E8%A7%A3Ax%3D0-%E4%B8%BB%E5%8F%98%E9%87%8F-%E7%89%B9%E8%A7%A3.md)
- [08. **求解Ax=b:可解性和解的结构**](https://github.com/chenyyx/notes-linear-algebra/tree/master/08-%E6%B1%82%E8%A7%A3Ax%3Db-%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84)
	 - [08.01 可解性](https://github.com/chenyyx/notes-linear-algebra/blob/master/08-%E6%B1%82%E8%A7%A3Ax%3Db-%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84/08-%E6%B1%82%E8%A7%A3Ax%3Db-%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84.md)
	 - [08.02 解的结构](https://github.com/chenyyx/notes-linear-algebra/blob/master/08-%E6%B1%82%E8%A7%A3Ax%3Db-%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84/08-%E6%B1%82%E8%A7%A3Ax%3Db-%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84.md)
- [09. **线性相关性、基、维数**](https://github.com/chenyyx/notes-linear-algebra/tree/master/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0)
	 - [09.01 线性相关性](https://github.com/chenyyx/notes-linear-algebra/blob/master/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0.md)
	 - [09.02 基](https://github.com/chenyyx/notes-linear-algebra/blob/master/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0.md)
	 - [09.03 维数](https://github.com/chenyyx/notes-linear-algebra/blob/master/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0/09-%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7-%E5%9F%BA-%E7%BB%B4%E6%95%B0.md)
- [10. **四个基本子空间**](https://github.com/chenyyx/notes-linear-algebra/tree/master/10-%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4)
	 - [10.01 基本子空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/10-%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4/10-%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4.md)
	 - [10.02 四个基本子空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/10-%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4/10-%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4.md)
- [11. **矩阵空间、秩1矩阵和小世界图**](https://github.com/chenyyx/notes-linear-algebra/tree/master/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE)
	 - [11.01 矩阵空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE.md)
	 - [11.02 秩1矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE.md)
	 - [11.03 小世界图](https://github.com/chenyyx/notes-linear-algebra/blob/master/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE/11-%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4-%E7%A7%A91%E7%9F%A9%E9%98%B5%E5%92%8C%E5%B0%8F%E4%B8%96%E7%95%8C%E5%9B%BE.md)
- [12. **图和网络**](https://github.com/chenyyx/notes-linear-algebra/tree/master/12-%E5%9B%BE%E5%92%8C%E7%BD%91%E7%BB%9C)
	 - [12.01 图](https://github.com/chenyyx/notes-linear-algebra/blob/master/12-%E5%9B%BE%E5%92%8C%E7%BD%91%E7%BB%9C/12-%E5%9B%BE%E5%92%8C%E7%BD%91%E7%BB%9C.md)
	 - [12.02 网络](https://github.com/chenyyx/notes-linear-algebra/blob/master/12-%E5%9B%BE%E5%92%8C%E7%BD%91%E7%BB%9C/12-%E5%9B%BE%E5%92%8C%E7%BD%91%E7%BB%9C.md)
- [13. **复习一**](https://github.com/chenyyx/notes-linear-algebra/tree/master/13-%E5%A4%8D%E4%B9%A0%E4%B8%80)
	 - [13.01 复习一](https://github.com/chenyyx/notes-linear-algebra/blob/master/13-%E5%A4%8D%E4%B9%A0%E4%B8%80/13-%E5%A4%8D%E4%B9%A0%E4%B8%80.md)
- [14. **正交向量与子空间**](https://github.com/chenyyx/notes-linear-algebra/tree/master/14-%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4)
	 - [14.01 正交向量](https://github.com/chenyyx/notes-linear-algebra/blob/master/14-%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4/14-%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4.md)
	 - [14.02 子空间](https://github.com/chenyyx/notes-linear-algebra/blob/master/14-%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4/14-%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4.md)
- [15. **子空间投影**](https://github.com/chenyyx/notes-linear-algebra/tree/master/15-%E5%AD%90%E7%A9%BA%E9%97%B4%E6%8A%95%E5%BD%B1)
	 - [15.01 子空间投影](https://github.com/chenyyx/notes-linear-algebra/blob/master/15-%E5%AD%90%E7%A9%BA%E9%97%B4%E6%8A%95%E5%BD%B1/15-%E5%AD%90%E7%A9%BA%E9%97%B4%E6%8A%95%E5%BD%B1.md)
- [16. **投影矩阵和最小二乘**](https://github.com/chenyyx/notes-linear-algebra/tree/master/16-%E6%8A%95%E5%BD%B1%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98)
	 - [16.01 投影矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/16-%E6%8A%95%E5%BD%B1%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98/16-%E6%8A%95%E5%BD%B1%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98.md)
	 - [16.02 最小二乘](https://github.com/chenyyx/notes-linear-algebra/blob/master/16-%E6%8A%95%E5%BD%B1%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98/16-%E6%8A%95%E5%BD%B1%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%98.md)
- [17. **正交矩阵和Gram-Schmidt正交化**](https://github.com/chenyyx/notes-linear-algebra/tree/master/17-%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%E6%AD%A3%E4%BA%A4%E5%8C%96)
	 - [17.01 正交矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/17-%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%E6%AD%A3%E4%BA%A4%E5%8C%96/17-%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%E6%AD%A3%E4%BA%A4%E5%8C%96.md)
	 - [17.02 Gram-Schmidt正交化](https://github.com/chenyyx/notes-linear-algebra/blob/master/17-%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%E6%AD%A3%E4%BA%A4%E5%8C%96/17-%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%E6%AD%A3%E4%BA%A4%E5%8C%96.md)
- [18. **行列式及其性质**](https://github.com/chenyyx/notes-linear-algebra/tree/master/18-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%8A%E5%85%B6%E6%80%A7%E8%B4%A8)
	 - [18.01 行列式](https://github.com/chenyyx/notes-linear-algebra/blob/master/18-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%8A%E5%85%B6%E6%80%A7%E8%B4%A8/18-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%8A%E5%85%B6%E6%80%A7%E8%B4%A8.md)
	 - [18.02 行列式性质](https://github.com/chenyyx/notes-linear-algebra/blob/master/18-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%8A%E5%85%B6%E6%80%A7%E8%B4%A8/18-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%8F%8A%E5%85%B6%E6%80%A7%E8%B4%A8.md)
- [19. **行列式公式和代数余子式**](https://github.com/chenyyx/notes-linear-algebra/tree/master/19-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%85%AC%E5%BC%8F%E5%92%8C%E4%BB%A3%E6%95%B0%E4%BD%99%E5%AD%90%E5%BC%8F)
	 - [19.01 行列式公式](https://github.com/chenyyx/notes-linear-algebra/blob/master/19-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%85%AC%E5%BC%8F%E5%92%8C%E4%BB%A3%E6%95%B0%E4%BD%99%E5%AD%90%E5%BC%8F/19-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%85%AC%E5%BC%8F%E5%92%8C%E4%BB%A3%E6%95%B0%E4%BD%99%E5%AD%90%E5%BC%8F.md)
	 - [19.02 代数余子式](https://github.com/chenyyx/notes-linear-algebra/blob/master/19-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%85%AC%E5%BC%8F%E5%92%8C%E4%BB%A3%E6%95%B0%E4%BD%99%E5%AD%90%E5%BC%8F/19-%E8%A1%8C%E5%88%97%E5%BC%8F%E5%85%AC%E5%BC%8F%E5%92%8C%E4%BB%A3%E6%95%B0%E4%BD%99%E5%AD%90%E5%BC%8F.md)
- [20. **克拉默法则、逆矩阵、体积**](https://github.com/chenyyx/notes-linear-algebra/tree/master/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF)
	 - [20.01 克拉默法则](https://github.com/chenyyx/notes-linear-algebra/blob/master/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF.md)
	 - [20.02 逆矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF.md)
	 - [20.03 体积](https://github.com/chenyyx/notes-linear-algebra/blob/master/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF/20-%E5%85%8B%E6%8B%89%E9%BB%98%E6%B3%95%E5%88%99-%E9%80%86%E7%9F%A9%E9%98%B5-%E4%BD%93%E7%A7%AF.md)
- [21. **特征值和特征向量**](https://github.com/chenyyx/notes-linear-algebra/tree/master/21-%E7%89%B9%E5%BE%81%E5%80%BC%E5%92%8C%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F)
	 - [21.01 特征值和特征向量](https://github.com/chenyyx/notes-linear-algebra/blob/master/21-%E7%89%B9%E5%BE%81%E5%80%BC%E5%92%8C%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F/21-%E7%89%B9%E5%BE%81%E5%80%BC%E5%92%8C%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F.md)
- [22. **对角化和A的幂**](https://github.com/chenyyx/notes-linear-algebra/tree/master/22-%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8CA%E7%9A%84%E5%B9%82)
	 - [22.01 对角化](https://github.com/chenyyx/notes-linear-algebra/blob/master/22-%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8CA%E7%9A%84%E5%B9%82/22-%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8CA%E7%9A%84%E5%B9%82.md)
	 - [22.02 A的幂](https://github.com/chenyyx/notes-linear-algebra/blob/master/22-%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8CA%E7%9A%84%E5%B9%82/22-%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8CA%E7%9A%84%E5%B9%82.md)
- [23. **微分方程和exp(At)**](https://github.com/chenyyx/notes-linear-algebra/tree/master/23-%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At))
	 - [23.01 微分方程](https://github.com/chenyyx/notes-linear-algebra/blob/master/23-%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At)/23-%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At).md)
	 - [23.02 exp(At)](https://github.com/chenyyx/notes-linear-algebra/blob/master/23-%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At)/23-%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At).md)
- [24. **马尔可夫矩阵;傅立叶级数**](https://github.com/chenyyx/notes-linear-algebra/tree/master/24-%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5-%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0)
	 - [24.01 马尔可夫矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/24-%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5-%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0/24-%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5-%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0.md)
	 - [24.02 傅立叶级数](https://github.com/chenyyx/notes-linear-algebra/blob/master/24-%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5-%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0/24-%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5-%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0.md)
- [25. **复习二**](https://github.com/chenyyx/notes-linear-algebra/tree/master/25-%E5%A4%8D%E4%B9%A0%E4%BA%8C)
	 - [25.01 复习二](https://github.com/chenyyx/notes-linear-algebra/blob/master/25-%E5%A4%8D%E4%B9%A0%E4%BA%8C/25-%E5%A4%8D%E4%B9%A0%E4%BA%8C.md)
- [26. **对称矩阵及正定性**](https://github.com/chenyyx/notes-linear-algebra/tree/master/26-%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7)
	 - [26.01 对称矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/26-%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7/26-%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7.md)
	 - [26.02 正定性](https://github.com/chenyyx/notes-linear-algebra/blob/master/26-%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7/26-%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7.md)
- [27. **复数矩阵和快速傅里叶变换**](https://github.com/chenyyx/notes-linear-algebra/tree/master/27-%E5%A4%8D%E6%95%B0%E7%9F%A9%E9%98%B5%E5%92%8C%E5%BF%AB%E9%80%9F%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2)
	 - [27.01 复数矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/27-%E5%A4%8D%E6%95%B0%E7%9F%A9%E9%98%B5%E5%92%8C%E5%BF%AB%E9%80%9F%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2/27-%E5%A4%8D%E6%95%B0%E7%9F%A9%E9%98%B5%E5%92%8C%E5%BF%AB%E9%80%9F%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2.md)
	 - [27.02 快速傅里叶变换](https://github.com/chenyyx/notes-linear-algebra/blob/master/27-%E5%A4%8D%E6%95%B0%E7%9F%A9%E9%98%B5%E5%92%8C%E5%BF%AB%E9%80%9F%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2/27-%E5%A4%8D%E6%95%B0%E7%9F%A9%E9%98%B5%E5%92%8C%E5%BF%AB%E9%80%9F%E5%82%85%E9%87%8C%E5%8F%B6%E5%8F%98%E6%8D%A2.md)
- [28. **正定矩阵和最小值**](https://github.com/chenyyx/notes-linear-algebra/tree/master/28-%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC)
	 - [28.01 正定矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/28-%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC/28-%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC.md)
	 - [28.02 最小值](https://github.com/chenyyx/notes-linear-algebra/blob/master/28-%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC/28-%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC.md)
- [29. **相似矩阵和若尔当形**](https://github.com/chenyyx/notes-linear-algebra/tree/master/29-%E7%9B%B8%E4%BC%BC%E7%9F%A9%E9%98%B5%E5%92%8C%E8%8B%A5%E5%B0%94%E5%BD%93%E5%BD%A2)
	 - [29.01 相似矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/29-%E7%9B%B8%E4%BC%BC%E7%9F%A9%E9%98%B5%E5%92%8C%E8%8B%A5%E5%B0%94%E5%BD%93%E5%BD%A2/29-%E7%9B%B8%E4%BC%BC%E7%9F%A9%E9%98%B5%E5%92%8C%E8%8B%A5%E5%B0%94%E5%BD%93%E5%BD%A2.md)
	 - [29.02 若尔当形](https://github.com/chenyyx/notes-linear-algebra/blob/master/29-%E7%9B%B8%E4%BC%BC%E7%9F%A9%E9%98%B5%E5%92%8C%E8%8B%A5%E5%B0%94%E5%BD%93%E5%BD%A2/29-%E7%9B%B8%E4%BC%BC%E7%9F%A9%E9%98%B5%E5%92%8C%E8%8B%A5%E5%B0%94%E5%BD%93%E5%BD%A2.md)
- [30. **奇异值分解**](https://github.com/chenyyx/notes-linear-algebra/tree/master/30-%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3)
	 - [30.01 奇异值分解](https://github.com/chenyyx/notes-linear-algebra/blob/master/30-%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3/30-%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3.md)
- [31. **线性变换及对应矩阵**](https://github.com/chenyyx/notes-linear-algebra/tree/master/31-%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E5%8F%8A%E5%AF%B9%E5%BA%94%E7%9F%A9%E9%98%B5)
	 - [31.01 线性变换](https://github.com/chenyyx/notes-linear-algebra/blob/master/31-%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E5%8F%8A%E5%AF%B9%E5%BA%94%E7%9F%A9%E9%98%B5/31-%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E5%8F%8A%E5%AF%B9%E5%BA%94%E7%9F%A9%E9%98%B5.md)
	 - [31.02 对应矩阵](https://github.com/chenyyx/notes-linear-algebra/blob/master/31-%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E5%8F%8A%E5%AF%B9%E5%BA%94%E7%9F%A9%E9%98%B5/31-%E7%BA%BF%E6%80%A7%E5%8F%98%E6%8D%A2%E5%8F%8A%E5%AF%B9%E5%BA%94%E7%9F%A9%E9%98%B5.md)
- [32. **基变换和图像压缩**](https://github.com/chenyyx/notes-linear-algebra/tree/master/32-%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9)
	 - [32.01 基变换](https://github.com/chenyyx/notes-linear-algebra/blob/master/32-%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9/32-%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9.md)
	 - [32.02 图像压缩](https://github.com/chenyyx/notes-linear-algebra/blob/master/32-%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9/32-%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9.md)
- [33. **复习三**](https://github.com/chenyyx/notes-linear-algebra/tree/master/33-%E5%A4%8D%E4%B9%A0%E4%B8%89)
	 - [33.01 复习三](https://github.com/chenyyx/notes-linear-algebra/blob/master/33-%E5%A4%8D%E4%B9%A0%E4%B8%89/33-%E5%A4%8D%E4%B9%A0%E4%B8%89.md)
- [34. **左右逆和伪逆**](https://github.com/chenyyx/notes-linear-algebra/tree/master/34-%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86)
	 - [34.01 左右逆](https://github.com/chenyyx/notes-linear-algebra/blob/master/34-%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86/34-%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86.md)
	 - [34.02 伪逆](https://github.com/chenyyx/notes-linear-algebra/blob/master/34-%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86/34-%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86.md)
- [35. **期末复习**](https://github.com/chenyyx/notes-linear-algebra/tree/master/35-%E6%9C%9F%E6%9C%AB%E5%A4%8D%E4%B9%A0)
	 - [35.01 期末复习](https://github.com/chenyyx/notes-linear-algebra/blob/master/35-%E6%9C%9F%E6%9C%AB%E5%A4%8D%E4%B9%A0/35-%E6%9C%9F%E6%9C%AB%E5%A4%8D%E4%B9%A0.md)

----

## 对应课程

![MIT_Linear-Algebra_1](/images/LA_whole_1.png)

![MIT_Linear-Algebra_2](/images/LA_whole_2.png)

CC/math

简介

发行版

贡献者

近期动态

CC/math .gitee-modal { width: 500px !important; }

简介

发行版

贡献者

近期动态

搜索帮助

CC/math