pca

When there's no exact solution, project. When data is high-dimensional, compress. The SVD is the Swiss Army knife that does both — and more. Master orthogonal projection, the normal equations, the Singular Value Decomposition, low-rank approximation, and the pseudoinverse.

Some vectors only get scaled by a matrix — they don't rotate at all. These eigenvectors reveal the skeleton of a linear transformation. Master the eigen-equation, the characteristic polynomial, diagonalization, and why eigenstructure powers PCA, PageRank, and stability analysis.