English | 日本語 | 中文(简体)

The-Art-of-Linear-Algebra

Graphic notes on Gilbert Strang’s “Linear Algebra for Everyone” by Kenji Hiranabe with the kindest help from Gilbert Strang. The output PDF files are listed below.

• The English version “The-Art-of-Linear-Algebra.pdf“
• The Japanese version “The-Art-of-Linear-Algebra-j.pdf“
• The Chinese version “The-Art-of-Linear-Algebra-zh-CN.pdf“ and “kf-liu/The-Art-of-Linear-Algebra-zh-CN/The-Art-of-Linear-Algebra-zh-CN.pdf“ for the latest Chinese version.

Abstract

I tried intuitive visualizations of important concepts introduced in “Linear Algebra for Everyone”.

This is aimed at promoting understanding of vector/matrix calculations and algorithms from the perspectives of matrix factorizations. They include Column-Row ( $CRCR$ ), Gaussian Elimination ( $LULU$ ), Gram-Schmidt Orthogonalization ( $QRQR$ ), Eigenvalues and Diagonalization ( $Q\mathrm{\Lambda }{Q}^{\mathrm{\top }}Q\backslash Lambda\; Q^\backslash top$), and Singular Value Decomposition ( $U\mathrm{\Sigma }{V}^{\mathrm{\top }}U\backslash Sigma\; V^\backslash top$ ).

Also includes other graphics.

Map of Eigenvalues

• Available in PDF “MapofEigenvalues“

Matrix World

• Available in PDF “MatrixWorld“

The Book 📕

The Japanese book of this paper has been published in 2026. Let me know if overseas publishers are interested in publishing this in English.

• https://anagileway.com/visual-linear-algebra/