├── .DS_Store ├── README.md ├── [01]方程组的几何解释 └── 线性代数[一].pdf ├── [02]矩阵消元 └── 线性代数[二].pdf ├── [03]乘法和逆矩阵 └── 线性代数[三].pdf ├── [04]A 的 LU 分解 ├── .DS_Store └── 线性代数[四].pdf ├── [05] 转置-转换-向量空间 R └── 线性代数[五].pdf ├── [06] 列空间和零空间 └── 列空间和零空间.pdf ├── [07] 求解 Ax = 0，主变量，特解 └── 线性代数[七].pdf ├── [08] Ax=b 的可解性和解的结构 └── 线性代数8.pdf ├── [09] 线性相关性，基，维数 └── 线性代数9.pdf ├── [10] 四个基本子空间 └── 线性代数10.pdf ├── [11] 矩阵空间 秩1 矩阵 └── 线性代数11.pdf ├── [12] 矩阵应用：图与网络 └── 线性代数12.pdf ├── [13] 复习一 └── 线性代数13.pdf ├── [14] 正交向量与子空间 └── 线性代数14.pdf ├── [15] 子空间投影 └── 线性代数15.pdf ├── [16] 投影矩阵和最小二乘 └── 线性代数16.pdf ├── [17] 正交矩阵和Gram-Schmidt 正交化 └── 线性代数17.pdf ├── [18,19] 行列式介绍 └── 线性代数18,19.pdf ├── [20] 克莱姆法则、逆矩阵、体积 └── 线性代数20.pdf ├── [21] 特征值和特征向量 └── 线性代数21.pdf ├── [22] 对角化和 A 的幂 └── 线性代数22.pdf ├── [23] 微分方程和exp(At) └── 线性代数23.pdf ├── [24] 马尔可夫矩阵;.傅立叶级数 └── 线性代数24.pdf ├── [25] 复习二 └── 线性代数25.pdf ├── [26] 对称矩阵及正定性 └── 线性代数26.pdf ├── [27] 复数矩阵和快速傅里叶变换 └── 线性代数27.pdf ├── [28] 正定矩阵和最小值 └── 线性代数28.pdf ├── [29] 相似矩阵和若尔当形 └── 线性代数29.pdf ├── [30] 奇异值分解 └── 线性代数30.pdf ├── [31] 线性变换及对应矩阵 └── 线性代数31.pdf ├── [32] 基变换和图像压缩 └── 线性代数32.pdf ├── [33] 单元检测3复习 └── 线性代数33.pdf ├── [34] 左右逆和伪逆 └── 线性代数34.pdf ├── [35] 期末复习 └── 线性代数35.pdf └── imgs ├── .DS_Store ├── cover ├── .DS_Store ├── 00.png ├── 01.png ├── 02.png ├── 03.png ├── 04.png ├── 05.png ├── 06.png ├── 07.png ├── 08.png ├── 09.png ├── 10.png ├── 11.png ├── 12.png ├── 13.png ├── 14.png ├── 15.png ├── 16.png ├── 17.png ├── 17_1.png ├── 18.png ├── 19.png ├── 20.png ├── 21.png ├── 22.png ├── 23.png ├── 24.png ├── 25.png ├── 26.png ├── 27.png ├── 28.png ├── 29.png ├── 30.png ├── 31.png ├── 32.png └── 33.png ├── icon ├── .DS_Store ├── ai.png ├── heart.png ├── intro.png ├── la.png ├── motivation.png ├── notes.png ├── organizer.png └── resource.png └── profile ├── .DS_Store ├── fuxuan_wei.png ├── kunbo_ding.png ├── libo_qin.png ├── shijue_huang.png ├── tianbao_xie.png └── xinyu_chen.png /.DS_Store: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MLNLP-World/MIT-Linear-Algebra-Notes/ffcd4122950960010e83f85b4dd57c735438ee8b/.DS_Store -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 |

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《麻省理工公开课：线性代数》中文笔记

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5 | 6 | version 7 | 8 | 9 | Status-building 10 | 11 | 12 | PRs-Welcome 13 | 14 | 15 | stars 16 | 17 | 18 | FORK 19 | 20 | 21 | Issues 22 | 23 |
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27 | 项目动机/ 28 | 课程简介/ 29 | 课程资源/ 30 | 笔记/ 31 | 组织者/ 32 | 贡献者 33 |

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35 | 36 | 37 | 38 | --- 39 | 40 | ## 项目动机 41 | 42 | 《麻省理工公开课：线性代数》是麻省理工公开课中广为流传的一门好课。本项目总结了我们在学习MIT线性代数课程 [Linear Algebra](http://open.163.com/special/opencourse/daishu.html)的学习笔记。赠人玫瑰，手留余香，我们将所有的笔记开源，希望在自己学习的同时，也对大家学习掌握《麻省理工公开课：线性代数》有所帮助。 43 | 44 | >本项目的特色： 45 | > 46 | >1. **笔记**与**原课程视频**一一对应，可以帮助大家一边听课一边理解。 47 | >2. 通过**图解**来使得笔记尽量通俗易懂 48 | 49 | 课程视频共35节，单个视频平均时长不超过60分钟，预计一个月可以学习完毕。 50 | 51 | 本项目所用徽章来自互联网，如侵犯了您的图片版权请联系我们删除，谢谢。 52 | 并且由于我们的水平有限，有任何问题和错误请批评指正，谢谢。 53 | 54 | ## 课程简介 55 | 56 | 57 | 课程介绍：“线性代数”，同微积分一样，是高等数学中两大入门课程之一，不仅是一门非常好的数学课程，也是一门非常好的工具学科，在很多领域都有广泛的用途。它的研究对象是向量，向量空间（或称线性空间），线性变换和有限维的线性方程组。本课程讲述了矩阵理论及线性代数的基本知识，侧重于那些与其他学科相关的内容，包括方程组、向量空间、行列式、特征值、相似矩阵及正定矩阵。 58 | 59 | ## 课程资源 60 | 61 | - 网易公开课网址：[麻省理工公开课：线性代数](https://open.163.com/newview/movie/courseintro?newurl=%2Fspecial%2Fopencourse%2Fdaishu.html) 62 | 63 | ## 笔记 64 | | 章节 | 视频 | 笔记 | 65 | | :------------------------------------- | :----------------------------------------------------------- | :----------------------------------------------------------- | 66 | | 第一课：方程组的几何解释 | | [方程组的几何解释](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/master/%5B01%5D%E6%96%B9%E7%A8%8B%E7%BB%84%E7%9A%84%E5%87%A0%E4%BD%95%E8%A7%A3%E9%87%8A/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E4%B8%80%5D.pdf) | 67 | | 第二课：矩阵消元 | | [矩阵消元](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/master/%5B02%5D%E7%9F%A9%E9%98%B5%E6%B6%88%E5%85%83/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E4%BA%8C%5D.pdf) | 68 | | 第三课：乘法和逆矩阵 | | [乘法和逆矩阵](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/master/%5B03%5D%E4%B9%98%E6%B3%95%E5%92%8C%E9%80%86%E7%9F%A9%E9%98%B5/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E4%B8%89%5D.pdf) | 69 | | 第四课：A 的 LU 分解 | | [A 的 LU 分解](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/master/%5B04%5DA%20%E7%9A%84%20LU%20%E5%88%86%E8%A7%A3/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E5%9B%9B%5D.pdf) | 70 | | 第五课：转置-置换-向量空间R | | [转置-置换-向量空间R](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/master/%5B05%5D%20%E8%BD%AC%E7%BD%AE-%E8%BD%AC%E6%8D%A2-%E5%90%91%E9%87%8F%E7%A9%BA%E9%97%B4%20R/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E4%BA%94%5D.pdf) | 71 | | 第六课：列空间与零空间 | | [列空间与零空间](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/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/%E5%88%97%E7%A9%BA%E9%97%B4%E5%92%8C%E9%9B%B6%E7%A9%BA%E9%97%B4.pdf) | 72 | | 第七课：求解 Ax = 0，主变量，特解 | | [求解 Ax = 0，主变量，特解](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/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/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0%5B%E4%B8%83%5D.pdf) | 73 | | 第八课：求解Ax=b：可解性和解的结构 | | [求解Ax=b：可解性和解的结构](https://github.com/ML-NLPChina/MIT-Linear-Algebra-Notes/blob/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) | 74 | | 第九课：线性相关性、基、维数 | | [线性相关性、基、维数](https://github.com/ML-NLPChina/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) | 75 | | 第十课：四个基本子空间 | | [四个基本子空间](https://github.com/ML-NLPChina/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) | 76 | | 第十一课：矩阵空间、秩1矩阵和小世界图 | | [矩阵空间、秩1矩阵和小世界图](https://github.com/ML-NLPChina/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) | 77 | | 第十二课：图和网络 | | [图和网络](https://github.com/ML-NLPChina/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) | 78 | | 第十三课：复习一 | | [复习一](https://github.com/ML-NLPChina/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) | 79 | | 第十四课：正交向量与子空间 | | [正交向量与子空间](https://github.com/ML-NLPChina/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) | 80 | | 第十五课：子空间投影 | | [子空间投影](https://github.com/ML-NLPChina/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) | 81 | | 第十六课：投影矩阵和最小二乘 | | [投影矩阵和最小二乘](https://github.com/ML-NLPChina/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) | 82 | | 第十七课：正交矩阵和Gram-Schmidt正交化 | | [正交矩阵和Gram-Schmidt正交化](https://github.com/ML-NLPChina/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) | 83 | | 第十八课：行列式介绍1 | | [行列式介绍](https://github.com/ML-NLPChina/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) | 84 | | 第十九课：行列式介绍2 | | [行列式介绍](https://github.com/ML-NLPChina/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) | 85 | | 第二十课：克拉默法则、逆矩阵、体积 | | [克拉默法则、逆矩阵、体积](https://github.com/ML-NLPChina/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) | 86 | | 第二十一课：特征值和特征向量 | | [特征值和特征向量](https://github.com/ML-NLPChina/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) | 87 | | 第二十二课：对角化和 A 的幂 | | [对角化和 A 的幂](https://github.com/ML-NLPChina/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) | 88 | | 第二十三课：微分方程和exp(At) | | [微分方程和exp(At)](https://github.com/ML-NLPChina/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) | 89 | | 第二十四课：马尔可夫矩阵;傅立叶级数 | | [马尔可夫矩阵;傅立叶级数](https://github.com/ML-NLPChina/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) | 90 | | 第二十五课：复习二 | | [复习二](https://github.com/ML-NLPChina/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) | 91 | | 第二十六课：对称矩阵及正定性 | | [对称矩阵及正定性](https://github.com/ML-NLPChina/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) | 92 | | 第二十七课：复数矩阵和快速傅里叶变换 | | [复数矩阵和快速傅里叶变换](https://github.com/ML-NLPChina/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) | 93 | | 第二十八课：正定矩阵和最小值 | | [正定矩阵和最小值](https://github.com/ML-NLPChina/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) | 94 | | 第二十九课：相似矩阵和若尔当形 | | [相似矩阵和若尔当形](https://github.com/ML-NLPChina/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) | 95 | | 第三十课：奇异值分解 | | [奇异值分解](https://github.com/ML-NLPChina/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) | 96 | | 第三十一课：线性变换及对应矩阵 | | [线性变换及对应矩阵](https://github.com/ML-NLPChina/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) | 97 | | 第三十二课：基变换和图像压缩 | | [基变换和图像压缩](https://github.com/ML-NLPChina/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) | 98 | | 第三十三课：单元检测3复习 | | [单元检测3复习](https://github.com/ML-NLPChina/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) | 99 | | 第三十四课：左右逆和伪逆 | | [左右逆和伪逆](https://github.com/ML-NLPChina/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) | 100 | | 第三十五课：期末复习 | | [期末复习](https://github.com/ML-NLPChina/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) | 101 | 102 | 103 | 104 | ## 组织者 105 | 感谢以下同学对本项目的组织 106 | 107 | 108 | 109 | ## 贡献者 110 | 感谢以下同学对本项目的支持与贡献 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 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