# Topics - Cholesky, LU, QR, polar, SVD decompositions. - Constrained, regularized, unconstrained least squares. Matrix norms and procrustes problems. - Dimensionality reduction and low-rank approximation: EYM theorem, PCA, regularized LRA, SURE, OptShrink, multidimensional scaling. - Companion matrices, minimal polynomials, vandermonde matrices, kronecker sums and products, power iteration, Perron-Frobenius theorems. - Irreducible matrices, Markov chains, spectral clustering. - Convex and nonconvex optimization, convergence of iterative algorithms, matrix completion.