Math & Optimization · beginner · concept 38 of 176
Linear Algebra for ML
The substrate everything runs on: data is vectors, models are matrices, and a forward pass is matrix multiplication. You need a working feel for dot products, matrix shapes, and eigenvectors, not proofs. GPUs exist because this one operation dominates all of AI. SVD, the workhorse matrix decomposition, is the machinery behind PCA and the low-rank idea LoRA reuses.
Key terms
VectorMatrix multiplicationDot productEigenvaluesRankSVD (singular value decomposition)
Where you meet it in the real world
Every single forward pass, embeddings, attention, PCA, graphics, and the GPU market
Videos
▶ Vectors | Chapter 1, Essence of linear algebra ↗
3Blue1Brown · YouTube
▶ Essence of linear algebra preview ↗
3Blue1Brown · YouTube
Guides and articles
Mathematics for Machine Learning | Companion webpage to the book “Mathematics for Machine ↗
Mathematics for Machine Learning (free book)
3Blue1Brown ↗
3Blue1Brown (site)
Courses, papers, and more
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