The math of AI, drawn and coded. A free, community-grown linear algebra course for people building AI, live at linearly.space.
Every lecture teaches the same idea four ways:
- Slides: the visual narrative, in a fast built-in viewer
- Article: a plain-language explanation written to be understood on the first pass
- Drawings: hand-drawn diagrams, shown exactly as drawn; every one on the site is the
1:1 export of an Excalidraw source in
drawings/ - Code: the concept executed in NumPy, PyTorch, JAX, and TensorFlow
The course is a reading companion to MIT 18.06: every lecture maps to Strang's lectures and Introduction to Linear Algebra (6th ed.). The original lectures were written and taught live in 2022 and 2023, before the LLM era; every explanation was worked out by hand for a room of real students.
| Part | Lectures | Status |
|---|---|---|
| I. Foundations | 00 How machines learn, 01 Vectors & dimensions, 02 Matrices & transformations, 03 NumPy & tensors | live |
| II. Solving Ax = b | 04 Elimination, 05 The algebra of matrices, 06 Factorizations A = CR and A = LU | live |
| III. Vector Spaces | 07 Vector spaces & subspaces, 7.5 The null space, 08 The complete solution & rank, 09 The four subspaces & the rank theorem | live |
| IV. Orthogonality | 10 Orthogonal subspaces, 11 Projections, 12 Least squares, 13 Gram–Schmidt & QR | live |
| V. Determinants & Eigenvalues | 14 Determinants, 15 Eigenvalues & positive definiteness | live |
| VI. The Missing Third | 16–22: SVD, pseudoinverse, low-rank & PCA, complex eigenvalues, Fourier, convolution, capstone | planned |
Also on the site: the roadmap, an honest staged path for learning this subject, and the library, a hard-curated shelf of the best books, videos, and tools, each with a note on how it teaches.
linearly started as one person's lecture series, but it is written and organized so a community can carry it further: one file per lecture, a documented path for every kind of contribution, and a style guide that keeps a hundred authors sounding like one course. If you learned something here and see how to teach it better, that belongs in the course. Everyone who has improved it appears on the contributors page, rebuilt from this repository's history on every deploy.
- CONTRIBUTING.md: how to fix, improve, and extend the course
- CODE_OF_CONDUCT.md: how we work together
- AGENTS.md: the full rulebook for AI coding agents working on this repo
pnpm install
pnpm dev # local dev server
pnpm build # production build + search indexRequires Node ≥ 22. The stack: Astro (static output), MDX content,
build-time KaTeX math, Shiki dual-theme code highlighting, Pagefind search, zero client-side
frameworks. Astro is pinned in package.json (see the note in .npmrc about release-cooldown
policies).
src/content/lectures/ ← one .mdx file per lecture (the article + front matter)
src/components/ ← SlideViewer, CodeTabs, Callout, Figure, playgrounds, …
src/assets/hero-art.svg ← generated identity art (pnpm exec node scripts/generate-art.mjs)
src/pages/ ← home, lectures, roadmap, resources, about
public/slides/<deck>/ ← optimized WebP slide images (1.webp … N.webp)
scripts/ ← slide pipeline (macOS) + hero-art and thumbnail generators
drawings/ ← Excalidraw sources for every diagram
The visual language is neobrutalist, adapted from
Brutal by Elian Van Cutsem (MIT). Diagrams are drawn in
Excalidraw; sources live in drawings/.
If this course is useful in your teaching, writing, or research, cite it. GitHub's "Cite this repository" button generates the reference from CITATION.cff, or copy:
Khalilli, A. and the linearly contributors. linearly: the math of AI, drawn and coded. https://linearly.space
This project is free for individuals, classrooms, and research, and all of its source is public. It is not available for commercial use: nobody may sell it, paywall it, or build paid products from it, and every adaptation must stay under the same terms.
- Code (components, scripts, styling): PolyForm Noncommercial 1.0.0
- Content (articles, drawings, slides, exercises): CC BY-NC-SA 4.0
If you are unsure whether your use counts as commercial, open an issue and ask.
This project is dedicated to Aqshin, one of the very first Azerbaijani students to study computer science at MIT, and the friend who told me about MIT OpenCourseWare in 2015. That conversation set everything here in motion.
© 2026 Ali Khalilli and the linearly contributors