Matrix Theory (III)

Abstract

AbstractEigenvalues and singular values are the main theme in this series of talks. Following Jordan's canonical form, we will briefly introduce in the first two talks some well-known results like Schur's Decomposition Theorem, Gersgorin Theorem for location of eigenvalues, numerical range, Kronecker product and Hadamard product.??Continuity arguments and block matrix techniques will be demonstrated. Ergodic Theorems for finite-state Markov chains will be shown as an application of the Perron-Frobenius Theorem for non-negative matrices. In the last two talks we mainly discuss Hermitian matrices. There are many interesting inequalities on the eigenvalues and determinants of this special class.