#svd
4 articles
01
·Linear Algebra·★ MEMBER·13 min read
A Tour of Matrix Decompositions — When to Reach for LU, QR, Cholesky, or SVD
A decomposition rewrites one awkward transformation as a product of parts you can actually work with: solve it (LU), solve it at half price (Cholesky), orthogonalize and fit (QR), or survive a broken matrix (SVD). Starting from why nobody computes an inverse, this piece builds up to a single table that tells you which one to reach for, plus the numpy that goes with it.
02
·Linear Algebra·FREE·7 min read
The Linear Algebra Under LoRA and RAG — Eigenvalues, Low Rank and Vector Search, Hands On
A matrix is a deformation of space, an eigenvector is a direction that survives it, SVD generalises the idea, and the dot product is the definition of 'similar'. Four interactive figures and four equations show that LoRA's ΔW=BA and RAG's vector search stand on the same floor. A column meant to be dragged, not just read.
03
·Linear Algebra·★ MEMBER·PAPER·10 min read
Singular Value Decomposition and Low-Rank Approximation — the Math Behind LoRA
Starting from the 'rotate, stretch, rotate' picture, this article builds Singular Value Decomposition (SVD) from zero: matrices as stacks of rank-1 layers, why real-world data needs only a few of them, and how that single fact lets LoRA fine-tune a giant model with 0.4% of the parameters.
04
·Linear Algebra·FREE·9 min read
Linear Algebra for AI — What Vectors and Matrices Are Actually Doing
You will never compute a determinant to read an AI paper. What you do need is two ideas: a vector is a coordinate where meaning lives, and a matrix is a machine that carries coordinates somewhere else. From why a dot product means similarity to reading the attention equation symbol by symbol.