Similarities and canonical forms of matrices, Normal, Hermitian and positive definite matrices. Matrix norms. Inequalities of eigenvalues and singular values.

CILO-1: Describe and use different classical canonical forms, including Schur triangularization and Jordan canonical form. CILO-2: Examine and apply the properties of normal and Hermitian matrices. CILO-3: Describe and use various decompositions, including the spectral decomposition and singular values decomposition. CILO-4: Examine and apply various inequalities involving norms, eigenvalues, and singular values.