The Art of Linear Algebra: Hiranabe's Graphic Notes on Strang's Linear Algebra for Everyone

What Hiranabe's notes solve, and who they are for

The repository holds graphic notes on Gilbert Strang's Linear Algebra for Everyone, made by Kenji Hiranabe with help from Strang. The README describes the aim plainly: to promote understanding of vector and matrix calculations from the perspective of matrix factorizations. Five are named: Column-Row (CR), Gaussian Elimination (LU), Gram-Schmidt Orthogonalization (QR), Eigenvalues and Diagonalization (Q Lambda Q transpose), and Singular Value Decomposition (U Sigma V transpose).

The audience is narrow and specific. If you are reading Strang's book, or sitting in a course that follows it, and the algebra of factorizations is not yet a picture in your head, these diagrams are the missing layer. If you have never seen a matrix multiply, the notes will not teach you that first step. They annotate a book; they do not replace one. The README also points to a Japanese book of the paper, published in 2026, and asks whether overseas publishers are interested in an English edition. So the repository is the free version of a project that has since become a printed book in one language.

How the graphic notes are built: LaTeX, figures and a makefile

The output is a PDF, and the repository shows how it is produced. The-Art-of-Linear-Algebra.tex is the main source, with per-language variants for Japanese and Simplified Chinese. A figs/ directory holds the figure sources, and figs-catalog.tex and figs-catalog.pdf collect them for browsing. The makefile drives the build, and name-list.mak and name-list-book.mak look like the lists of names used in the paper and the book edition.

The primary language is listed as PostScript, which reflects the figure pipeline rather than the text. The diagrams also ship as PNG and PPTX: 5-Factorizations.png, MapofEigenvalues.png, MatrixWorld.png, plus Graphic-Notes-on-LA4E-v1.1.pptx and Illustrations.pptx. That matters for how you use it. The PDF is the reading artifact, the PNG files are for slides and notes, and the PPTX files are for editing the drawings yourself. There is no application, no library and no API. It is a document repository with reproducible sources, and the data flow is one direction: LaTeX plus figures in, PDF out.

Installing nothing: reading the PDF and building it from source

There is no package to install. The README lists the output files directly, and the fastest path is to open the English PDF from the repository. If you want the printable or slide-ready versions, the same directory holds the PPTX and PNG files.

If you want to rebuild or edit the notes, you need a LaTeX toolchain, because the sources are .tex files. Clone the repository and run the makefile target for the document:

make The-Art-of-Linear-Algebra.pdf

The repository's makefile is the entry point for the build, and the .tex files are the inputs. The README does not document the required LaTeX distribution or the exact target names, so check the makefile before you run anything. Expect the figure sources under figs/ to be part of the build.

For a first real use, you do not need the build at all. Open The-Art-of-Linear-Algebra.pdf and read the page for the factorization you are currently studying. The 5-Factorizations.png image in the README is the same diagram in image form, and it is the natural starting point if you only want to see how the five factorizations relate.

Where the notes stop: no exercises, no proofs, no rollback story

The README is short and does not describe a workflow, a versioning policy or a contribution process. There are no releases listed. The repository is not archived, and the last push was on 2026-09-18, so the sources are current, but currency is not the same as documentation depth.

The real limitation is scope. This is a set of illustrations for one book. It does not contain exercises, solutions, proofs or a syllabus. If your course uses a different notation for the SVD or orders the factorizations differently, the diagrams may not line up with your lecture notes, and there is no configuration to change that beyond editing the LaTeX yourself. It is also the wrong tool if you want interactive exploration: there is no notebook, no code, no plotting library. A student who needs to compute a factorization rather than picture it should be in NumPy or a similar environment, not in this repository. And the README does not document how to regenerate the translated PDFs or how the Chinese version is kept in sync, beyond pointing at a separate repository for the latest Chinese PDF.

Compared with a textbook or a notebook-based course

The obvious alternative is the book itself. Strang's Linear Algebra for Everyone is the source text, and the notes are explicitly derived from it. The difference in approach is that the book builds the argument in prose and exercises, while Hiranabe's notes compress the same concepts into diagrams of the factorizations. You read the book to learn; you look at the notes to see.

A second alternative is a computational course built on notebooks, where you enter a matrix and watch the factorization happen numerically. That teaches a different skill: recognizing when a decomposition is stable, and what the matrices look like at a realistic size. The graphic notes teach the shape of the idea, not its numerical behavior. Neither approach subsumes the other, and the honest use of this repository is as a companion to one of them, not as a substitute. The repository's own README frames it as promoting understanding of the algorithms through the factorization view, which is a companion's job description.

Licence, maintenance and the cost of keeping a fork

The licence is CC0-1.0, which places the work in the public domain as far as the licence goes. For a reader, that means you can copy the diagrams into your own notes or slides without asking. For anyone planning to redistribute or translate, it removes the usual attribution requirement, though the README itself credits Hiranabe and Strang, and keeping that credit is the decent thing even when the licence does not demand it. This is a description of the licence text, not legal advice.

Maintenance cost is low because there is nothing to run. The upgrade cost is the interesting part: the repository is a set of documents, so an update means re-reading or re-downloading a PDF, not migrating an API. If you fork the LaTeX to adapt the notes for your own course, you inherit the build, and the makefile and .tex sources are the whole surface area. The repository does not document a release process, so there is no changelog to follow. The Chinese translation lives partly in a separate repository, kf-liu/The-Art-of-Linear-Algebra-zh-CN, which the README names as the source of the latest Chinese PDF; that split is the main coordination cost if you care about the translated editions.

Editorial conclusion

Use this repository if you already have Strang's book or a course using it and want a visual index of CR, LU, QR, Q Lambda Q transpose and U Sigma V transpose before you work the exercises. Do not use it as a first course in linear algebra, and do not expect worked problems or proofs, because the repository contains graphics and LaTeX sources, not a curriculum. Before you rely on it, open The-Art-of-Linear-Algebra.pdf and check that the factorization diagrams match the notation your course uses.

Frequently asked questions

Official sources

1. Issues
2. kenjihiranabe/The-Art-of-Linear-Algebra on GitHub
3. License: CC0-1.0
4. README