Linear Algebra for AI — Part 1: What Is Linear Algebra? (The Big Picture)
Last updated: 23 Nov 2025
Linear algebra is the study of straight-line relationships and flat spaces — how things move, stretch, rotate, or combine without breaking structure.
It’s the language of transformations that keep:
- straight lines → straight
- parallel lines → parallel
- the origin → fixed
Think of it as the physics of predictable space.
Everything in AI lives here.
The Fundamental Building Blocks(Everything Stems From These)
| Concept | Everyday Meaning |
|---|---|
| Vector | Arrow with direction + length (or a meaningful list) |
| Matrix | Grid that transforms vectors — the “warp machine” |
| Scalar | Simple number that stretches/shrinks vectors |
| Linear Combination | Mixing scaled vectors (a·v₁ + b·v₂) |
| Span | All points you can reach with combinations |
| Basis | Smallest independent set that spans the space |
Determinants, eigenvalues, PCA, SVD, neural networks — all built on these six ideas.
Why Does AI Rely So Heavily on Linear Algebra?
AI = vectors pushed through matrices.
- Data points → vectors in high-dimensional space
- Neural network layers → matrices that transform those vectors
- Training → finding the best transformation
No linear algebra → no deep learning.
