Interactive lesson~20 minBeginner
Linear Algebra for ML
Linear algebra is the language models use to move information. Vectors hold meaning, matrices transform it, and eigendirections reveal what a transformation preserves.
EigenvaluesSVDMatrix multiply
Mental model
A matrix is a machine that stretches, rotates, compresses, and mixes space.
Every embedding lookup, attention projection, convolution, and optimizer step is matrix work wearing a different hat.
Compression
balanced56% modeled signal
Signal clarity
balanced53% modeled signal
Generalization
balanced55% modeled signal
Concept pipeline
Build the idea in four moves
Interactive lab
Tune a projection layer and watch what happens to representation quality.
Vectors
Represent examples as points with direction and magnitude.
Focus lens
The part that usually clicks late
Dot product
Measures alignment: positive means same direction, negative means opposition.
Compression
56
Signal clarity
53
Generalization
55
Knowledge check
Why does low-rank structure matter in ML?
Next horizon
Where this topic is headed
Randomized SVD
LoRA rank selection
Spectral regularization