# Matrix Decompositions: Eigendecomposition, SVD, PCA, and the Secret of LoRA

> Source: https://sukruyusufkaya.com/en/learn/llm-muhendisligi/matris-ayristirmalari-svd-eigen-pca-lora
> Updated: 2026-05-13T13:00:22.742Z
> Category: LLM Mühendisliği
> Module: Module 1: The AI Engineer's Mathematical Arsenal
**TLDR:** The art of decomposing a matrix into its 'DNA'. Eigendecomposition and SVD, building PCA from SVD from scratch, the mathematical foundation of LoRA — why low-rank updates suffice. Embedding compression practice.