Eigenvalues & Eigenvectors

Summary

Special vectors that only get scaled (not rotated) by a matrix transformation — the math underlying PCA, dimensionality reduction and understanding data variance.

• 1Compute eigenvalues/eigenvectors for a small 2x2 matrix by hand.
• 2Learn how PCA uses eigenvectors of the covariance matrix to find directions of maximum variance.
• 3Visualize how eigenvectors define the axes a linear transformation stretches along.