| Course Description : | Similarity and canonical forms, diagonalization and simultaneous diagondization of matrices, location of eigenvalues, special classes of matrices, unitary equivalence of matrices, Schur’s theorem and spectral theorem, singular value decomposition and polar decomposition, generalized inverses, least-squares solutions to linear systems, determinant and trace inequalities, the min-max principle, singular value inequalities, perturbation inequalities, vector and matrix norms, the spectral radius and the numerical radius, unitarily invariant norms, norm inequalities, the Löwner ordering of Hermitian matrices, Hadamard product of matrices, applications. |