Phase 2 · Math, when you need it · Linear algebra
Eigenvectors (intuition)
The directions a transformation leaves pointing the same way.
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Why it matters
When a matrix moves the points on a page, most arrows get knocked sideways. A few special arrows don't: the matrix only makes them longer or shorter. These are called eigenvectors, and they show what a matrix "really does". Google's original search ranking, PageRank, was one. PCA, which you'll use to shrink and plot embeddings, is built from them. You'll never need to calculate them by hand. You do need the picture, and that's what this lesson gives you.
What you'll be able to do
- Explain an eigenvector as a direction a matrix only stretches
- Check the equation Av = λv numerically
- Find the dominant eigenvector by repeatedly applying a matrix (power iteration)
- Connect eigenvectors to PageRank and to PCA
Before this lesson
Next in this phase: SVD and PCA