Hermitian Matrices

Abstract

Introduction: This chapter contains fundamental results of Hermi-tian matrices and demonstrates the basic techniques used to derive the results. Section 8.1 presents equivalent conditions to matrix Her-mitity, Section 8.2 gives some trace inequalities and discusses a necessary and sufficient condition for a square matrix to be a product of two Hermitian matrices, and Section 8.3 develops the min-max theorem and the interlacing theorem for eigenvalues. Section 8.4 deals with the eigenvalue and singular value inequalities for the sum of Her-mitian matrices, and Section 8.5 shows a matrix triangle inequality.