Linear Algebra 4 Every One

Copyright note, what I share below is a summary of the book " Linear Algebra for Everyone " written by Professor Gilbert Strang on github by a Japanese scholar named Kenji Hiranabe . It is more like a very beautiful linear Algebra Handbook, everyone is welcome to download and collect it. If there is any copyright infringement in this shared article of mine, I will delete the article immediately.

The publishing address of specific articles:

https://github.com/kenjihiranabe/The-Art-of-Linear-Algebra/blob/main/README-zh-CN.mdhttps://github.com/kenjihiranabe/The-Art-of-Linear-Algebra/blob/main/README-zh-CN.md

The article is available in English, Japanese and Chinese.

This is the personal official website of Grandpa Gilbert Strang of MIT:

Gilbert Strang's HomepageProf. Gilbert Strang's Home Page, MIT Math Dept. Containsrecent wavelet and applied math papers, textbooks, and shortcourseinformation.https://math.mit.edu/~gs/

This is the download address for his book " Linear Algebra for Everyone ":

Linear Algebra for Everyone, Gilbert Stranghttps://math.mit.edu/~gs/everyone/

All of the following are screenshots from the manual:

Author and preface

Four perspectives on understanding the matrix

Multiplication of vectors by vectors

Note: The description of v1 and v2 in the figure will be used later. v is the first letter of vector in English.

v1 represents the row vector times the column vector

v2 means column vector times row vector

Multiplication of matrices and vectors

Mv1 and Mv2 both represent matrix times column vector , Mv2 is the key point.

M and v are the first letters of Matrix in English and Vector in English respectively.

vM1 and vM2 both represent a row vector multiplied by a matrix, vM2 is the focus.

Understand matrices and matrix multiplication from four perspectives

MM1, MM2, MM3, and MM4 all represent matrix-matrix multiplication. Personally, I think MM2 and MM3 are the key points.

Another interpretation of matrix-matrix multiplication

Although the author said that P1 is a combination of MM2 and Mv2, I don't think so. I think in the above picture, P1 is MM2 and p2 is MM3. I just changed the illustration to illustrate.

Multiplication of matrices and diagonal matrices

Five ways to decompose a matrix

A=CR

A=LU

A=QR

$\Large \mathbf{S=Q\Lambda Q^{T}}$

$\Large \mathbf{A=U\Sigma V^{T}}$

Full map of eigenvalues

matrix world

(Full text ends)

Author---Panasonic J27

References (acknowledgments):

1，https://github.com/kf-liu/The-Art-of-Linear-Algebra-zh-CN/blob/main/The-Art-of-Linear-Algebra-zh-CN.pdf

2，https://github.com/kenjihiranabe/The-Art-of-Linear-Algebra/blob/main/README-zh-CN.md

(Put a screenshot of Grandpa Strang’s video)

Copyright statement: Some of the pictures, texts or other materials in this article may come from many different websites and descriptions. It is impossible to list them all here. If there is any infringement, please inform us and they will be deleted immediately. Everyone is welcome to reprint, but if someone quotes or copies my article, you must indicate in your article that the pictures or text you use come from my article, otherwise, infringement will be investigated. ----Panasonic J27