# MIT-Linear-Algebra-Notes

**Repository Path**: quminzi/MIT-Linear-Algebra-Notes

## Basic Information

- **Project Name**: MIT-Linear-Algebra-Notes
- **Description**: No description available
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
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- **Created**: 2021-05-17
- **Last Updated**: 2021-05-17

## Categories & Tags

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## README

# 18.06 线性代数（Linear Algebra）中文笔记

该笔记总结了我们在学习MIT线性代数课程的学习经验和过程。

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。

本笔记作者介绍：


丁坤博 东北大学本科生，推免至北京大学攻读研究生


覃立波 哈尔滨工业大学SCIR实验室在读博士生，导师车万翔老师 

## 笔记目录
第一课：01. 方程组的几何解释
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29E773)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/87873464)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%E6%96%B9%E7%A8%8B%E7%BB%84%E7%9A%84%E5%87%A0%E4%BD%95%E8%A7%A3%E9%87%8A)

第二课：02.矩阵消元
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29EGPP)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/88272838)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%E7%9F%A9%E9%98%B5%E6%B6%88%E5%85%83)

第三课：03.乘法和逆矩阵
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29FCHO)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/88755358)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%E4%B9%98%E6%B3%95%E5%92%8C%E9%80%86%E7%9F%A9%E9%98%B5)

第四课：04.A 的 LU 分解
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29FCHO)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/89784741)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%5B04%5DA%20%E7%9A%84%20LU%20%E5%88%86%E8%A7%A3)

第五课：转置-置换-向量空间R
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29FRJK)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/90227543)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%5B04%5DA%20%E7%9A%84%20LU%20%E5%88%86%E8%A7%A3)

第六课：列空间与零空间
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29FRJK)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/105280523)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%5B06%5D%20%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4)

第七课：求解 Ax = 0，主变量，特解
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V29FRJK)
* [知乎专栏笔记地址](https://zhuanlan.zhihu.com/p/106145156)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/tree/master/%5B07%5D%20%E6%B1%82%E8%A7%A3%20Ax%20%3D%200%EF%BC%8C%E4%B8%BB%E5%8F%98%E9%87%8F%EF%BC%8C%E7%89%B9%E8%A7%A3)

第八课：求解Ax=b：可解性和解的结构
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2ABHV8)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/raw/master/%5B08%5D%20Ax%3Db%20%E7%9A%84%E5%8F%AF%E8%A7%A3%E6%80%A7%E5%92%8C%E8%A7%A3%E7%9A%84%E7%BB%93%E6%9E%84/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B08.pdf)

第九课：线性相关性、基、维数
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2ACDCT)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B09%5D%20%E7%BA%BF%E6%80%A7%E7%9B%B8%E5%85%B3%E6%80%A7%EF%BC%8C%E5%9F%BA%EF%BC%8C%E7%BB%B4%E6%95%B0/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B09.pdf)

第十课：四个基本子空间
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2ADFDT)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B10%5D%20%E5%9B%9B%E4%B8%AA%E5%9F%BA%E6%9C%AC%E5%AD%90%E7%A9%BA%E9%97%B4/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B010.pdf)

第十一课：矩阵空间、秩1矩阵和小世界图
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AJS2T)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B11%5D%20%E7%9F%A9%E9%98%B5%E7%A9%BA%E9%97%B4%20%E7%A7%A91%20%E7%9F%A9%E9%98%B5/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B011.pdf)

第十二课：图和网络
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AIUTE)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B12%5D%20%E7%9F%A9%E9%98%B5%E5%BA%94%E7%94%A8%EF%BC%9A%E5%9B%BE%E4%B8%8E%E7%BD%91%E7%BB%9C/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B012.pdf)

第十三课：复习一
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AJ69K)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B13%5D%20%E5%A4%8D%E4%B9%A0%E4%B8%80/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B013.pdf)

第十四课：正交向量与子空间
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AJEMH)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B14%5D%20%E6%AD%A3%E4%BA%A4%E5%90%91%E9%87%8F%E4%B8%8E%E5%AD%90%E7%A9%BA%E9%97%B4/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B014.pdf)

第十五课：子空间投影
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AJLJU)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B15%5D%20%E5%AD%90%E7%A9%BA%E9%97%B4%E6%8A%95%E5%BD%B1/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B015.pdf)

第十六课：投影矩阵和最小二乘
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AOJPU)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B16%5D%20%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/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B016.pdf)

第十七课：正交矩阵和Gram-Schmidt正交化
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AORLS)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B17%5D%20%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5%E5%92%8CGram-Schmidt%20%E6%AD%A3%E4%BA%A4%E5%8C%96/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B017.pdf)

第十八 十九课：行列式介绍
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AP150)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B18%2C19%5D%20%E8%A1%8C%E5%88%97%E5%BC%8F%E4%BB%8B%E7%BB%8D/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B018%2C19.pdf)

第二十课：克拉默法则、逆矩阵、体积
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AQ40C)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B20%5D%20%E5%85%8B%E8%8E%B1%E5%A7%86%E6%B3%95%E5%88%99%E3%80%81%E9%80%86%E7%9F%A9%E9%98%B5%E3%80%81%E4%BD%93%E7%A7%AF/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B020.pdf)

第二十一课：特征值和特征向量
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AV2R8)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B21%5D%20%E7%89%B9%E5%BE%81%E5%80%BC%E5%92%8C%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B021.pdf)

第二十二课：对角化和 A 的幂 
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AV6GL)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B22%5D%20%E5%AF%B9%E8%A7%92%E5%8C%96%E5%92%8C%20A%20%E7%9A%84%E5%B9%82/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B022.pdf)

第二十三课：微分方程和exp(At)
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AVIBM)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B23%5D%20%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E5%92%8Cexp(At)/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B023.pdf)

第二十四课：马尔可夫矩阵;.傅立叶级数
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AVOAV)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B24%5D%20%E9%A9%AC%E5%B0%94%E5%8F%AF%E5%A4%AB%E7%9F%A9%E9%98%B5%3B.%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B024.pdf)

第二十五课：复习二
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M7E4C9V6P)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B25%5D%20%E5%A4%8D%E4%B9%A0%E4%BA%8C/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B025.pdf)

第二十六课：对称矩阵及正定性
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2AVUL4)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B26%5D%20%E5%AF%B9%E7%A7%B0%E7%9F%A9%E9%98%B5%E5%8F%8A%E6%AD%A3%E5%AE%9A%E6%80%A7/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B026.pdf)

第二十七课：复数矩阵和快速傅里叶变换
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2B4U77)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B27%5D%20%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/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B027.pdf)

第二十八课：正定矩阵和最小值
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2B5J3P)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B28%5D%20%E6%AD%A3%E5%AE%9A%E7%9F%A9%E9%98%B5%E5%92%8C%E6%9C%80%E5%B0%8F%E5%80%BC/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B028.pdf)

第二十九课：相似矩阵和若尔当形
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2B5OKE)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B29%5D%20%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/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B029.pdf)

第三十课：奇异值分解
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2B5R1G)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B30%5D%20%E5%A5%87%E5%BC%82%E5%80%BC%E5%88%86%E8%A7%A3/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B030.pdf)

第三十一课：线性变换及对应矩阵
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2B60PJ)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B31%5D%20%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/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B031.pdf)

第三十二课：基变换和图像压缩
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2BA04Q)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B32%5D%20%E5%9F%BA%E5%8F%98%E6%8D%A2%E5%92%8C%E5%9B%BE%E5%83%8F%E5%8E%8B%E7%BC%A9/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B032.pdf)

第三十三课：单元检测3复习
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2BA6N8)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B33%5D%20%E5%8D%95%E5%85%83%E6%A3%80%E6%B5%8B3%E5%A4%8D%E4%B9%A0/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B033.pdf)

第三十四课：左右逆和伪逆
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2BADQ9)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B34%5D%20%E5%B7%A6%E5%8F%B3%E9%80%86%E5%92%8C%E4%BC%AA%E9%80%86/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B034.pdf)

第三十五课：期末复习
* [中文字幕课程地址](http://open.163.com/newview/movie/free?pid=M6V0BQC4M&mid=M6V2BAN1H)
* [PDF下载地址](https://github.com/yizhen20133868/MIT-Linear-Algebra-Notes/blob/master/%5B35%5D%20%E6%9C%9F%E6%9C%AB%E5%A4%8D%E4%B9%A0/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B035.pdf)