The Little Book of Linear Algebra (little-book-of.github.io)

The Little Book of Linear Algebra is a compact, application-minded primer that collects the core linear-algebra concepts every AI/ML practitioner needs: vectors and geometry; matrices and their arithmetic; solving linear systems and elimination; subspaces, bases, and dimension; determinants and volume; eigenvalues/eigenvectors and dynamics; orthogonality, least squares and QR; and the SVD/PCA/conditioning trifecta — capped by practical applications and numerical concerns. It reads like a roadmap from basic notation to the matrix factorizations and stability diagnostics that underlie modern machine learning pipelines. For the AI/ML community the book matters because it ties mathematical ideas directly to algorithmic and computational realities: matrix–vector and matrix–matrix products as building blocks, Gaussian elimination and LU for solving systems, QR and Gram–Schmidt for stable least squares, SVD and PCA for low-rank approximation and dimensionality reduction, and pseudoinverses, regularization, and condition numbers for handling ill-posed problems. It also highlights applied topics — Markov chains, PageRank, recommender systems, camera/robotics transforms — and practical tools (cost counts, BLAS/LAPACK, rank-revealing factorizations). In short, it’s a concise technical reference that connects linear algebra theory to the numerical methods, stability issues, and model-reduction techniques central to building robust, scalable ML systems.