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Matrix Theory pp 208-239 | Cite as

Hermitian Matrices

  • Fuzhen Zhang
Part of the Universitext book series (UTX)

Abstract

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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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Fuzhen Zhang
    • 1
  1. 1.Department of Math, Science, and TechnologyNova Southeastern UniversityFort LauderdaleUSA

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