Course information

Vector norms, inner products, and the Cauchy-Schwarz inequality, continuity and equivalence of norms, matrix norms, induced norms, Schur’s triangularization, spectral radius, and norms. The Gram-Schmidt orthonormalization process and the simple QR decomposition. Singular value decomposition (SVD), singular values, low-rank approximations, pseudoinverse, and least squares problem. Normal matrices, stability of linear systems, and perturbation theory. Spectral analysis of positive and nonnegative matrices and their applications. Pseudospectrum definitions and its applications.