---
id:"kb-2026-00193"
title:"Linear Algebra"
schema_type:"TechArticle"
category:"computer-science"
language:"en"
confidence:"high"
last_verified:"2026-05-22"
generation_method: "human_only"
ai_models:["claude-opus"]
derived_from_human_seed:true


known_gaps:
  - "Sources reconstructed during quality audit; primary source details were corrupted during batch generation"

completeness: 0.88
ai_citations:
  last_citation_check:"2026-05-22"
primary_sources:
- title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
secondary_sources:
  - title: "ACM Digital Library"
    type: "repository"
    year: 2026
    url: "https://dl.acm.org/"
    institution: "ACM"
---

## TL;DR

Linear algebra is the mathematics of vectors and matrices, fundamental to computer graphics, machine learning (neural networks), physics simulation, and data science. Core concepts: vectors, matrices, linear transformations, determinants, eigenvalues/eigenvectors, linear systems.

## Core Explanation

Matrix multiplication: AB = C where C_ij = Σ A_ik * B_kj. Neural networks: forward pass is matrix multiplications with activation functions. Gradient descent: derivative of loss w.r.t. weights computed via backpropagation (chain rule on matrices). SVD (Singular Value Decomposition): A = UΣV^T — fundamental to PCA, recommendation systems, image compression.

## Further Reading

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