Eigenvalues, Quadratic Forms & SVD

Explore the geometry behind covariance matrices and statistical computation. Interpret quadratic forms, eigenvectors, spectral decompositions, singular values, rank and pseudoinverses. Prerequisites: matrix arithmetic, orthogonality and least squares. Worked examples and counterexamples connect variance directions with degeneracy, minimum-norm solutions and numerical tolerance without requiring advanced PCA theory.

Further reading: Positive semidefinite matrices, SVD reference.