## 那些值得推荐和收藏的线性代数学习资源

2019 年 3 月 6 日 AINLP

Introduction to Linear Algebra (3rd Ed.) by Gilbert Strang.

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/
(注：这里我修正了一下链接，原文链接已经没有了）

1. 麻省理工公开课：线性代数

http://open.163.com/special/opencourse/daishu.html

“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。

2. 3Blue1Brown: Essence of linear algebra（线性代数的本质）

https://www.bilibili.com/video/av5987715/

3. Immersive Linear Algebra

《英文版的线性代数电子书：Immersive Linear Algebra》该书是今天 Hacker News 首页头条。号称是全球第一个全交互式图形的线代电子书。

4. Matrix Algebra for Engineers

http://coursegraph.com/coursera-matrix-algebra-engineers

This course is all about matrices, and concisely covers the linear algebra that an engineer should know. We define matrices and how to add and multiply them, and introduce some special types of matrices. We describe the Gaussian elimination algorithm used to solve systems of linear equations and the corresponding LU decomposition of a matrix. We explain the concept of vector spaces and define the main vocabulary of linear algebra. We develop the theory of determinants and use it to solve the eigenvalue problem. After each video, there are problems to solve and I have tried to choose problems that exemplify the main idea of the lecture. I try to give enough problems for students to solidify their understanding of the material, but not so many that students feel overwhelmed and drop out. I do encourage students to attempt the given problems, but if they get stuck, full solutions can be found in the lecture notes for the course. The mathematics in this matrix algebra course is presented at the level of an advanced high school student, but typically students would take this course after completing a university-level single variable calculus course.

http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

5. Mathematics for Machine Learning: Linear Algebra

http://coursegraph.com/coursera-linear-algebra-machine-learning

In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. Finally we look at how to use these to do fun things with datasets – like how to rotate images of faces and how to extract eigenvectors to look at how the Pagerank algorithm works. Since we’re aiming at data-driven applications, we’ll be implementing some of these ideas in code, not just on pencil and paper. Towards the end of the course, you’ll write code blocks and encounter Jupyter notebooks in Python, but don’t worry, these will be quite short, focussed on the concepts, and will guide you through if you’ve not coded before. At the end of this course you will have an intuitive understanding of vectors and matrices that will help you bridge the gap into linear algebra problems, and how to apply these concepts to machine learning.

6. 可汗学院公开课：线性代数

http://open.163.com/special/Khan/linearalgebra.html

### 相关内容

【导读】MIT-Gilbert Strang教授讲解的线性代数奉为经典，在疫情期间85岁高龄的Strang教授对着摄像机出了新的课程：A 2020 Vision of Linear Algebra，老教授出神入化将许多人认为简单却是最基础的东西讲的出神入化。值得学习。

William Gilbert Strang，美国数学家，在有限元理论、变分法、小波分析和线性代数等方面皆有研究贡献。他对数学教育做出了许多贡献，包括出版七本数学教科书和专著。斯特朗现任麻省理工学院数学系 MathWorks 讲座教授。主要讲授课程为线性代数入门（Introduction to Linear Algebra，18.06）和计算科学与工程（Computational Science and Engineering，18.085），这些课程都可在麻省理工学院开放式课程中免费学习。

Bilibili（爱可可老师）：https://www.bilibili.com/video/BV1Ki4y147Kh

Part 1- 矩阵的列空间与向量空间中的基

Part 2- 线性代数的 Big Picture

Part 3- 正交向量

Part 4- 特征值与特征向量

Part 5- 奇异值与奇异向量

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