This chapter contains fundamental results of Hermitian matrices and demonstrates the basic techniques used to derive the results. Section 7.1 presents equivalent conditions to matrix Hermitity, Section 7.2 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 7.3 develops the min-max theorem and the interlacing theorem for eigenvalues. Section 7.4 deals with the eigenvalue and singular value inequalities for the sum of Hermitian matrices, and Section 7.5 shows a matrix triangle inequality.
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