Eigenvalues and Eigenvectors

The directions that survive a transformation unchanged

Eigenvectors are the directions a matrix only stretches (never rotates). Eigenvalues tell you how much. This module builds geometric intuition first -- watching vectors get transformed and identifying the special ones that stay on their line -- then covers the characteristic polynomial and diagonalization. The payoff: eigenvalues are the key to PCA, Google's PageRank, and stability analysis.

Estimated time: 60 minutes

Stuck on something? The AI tutor sees this lecture—just ask.