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. Mini-lab: Animate a 2x2 transformation showing all vectors being rotated except the eigenvectors, which only scale.

Estimated time: 60 minutes

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