Matrix Theory pp 159-207 | Cite as

Positive Semidefinite Matrices

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


This chapter studies the positive semidefinite matrices, concentrating primarily on the inequalities of this type of matrix. The main goal is to present the fundamental results and show some often-used techniques. Section 6.1 gives the basic properties, Section 6.2 treats the Löwner partial ordering of positive semidefinite matrices, and Section 6.3 presents some inequalities of principal submatrices. Section 6.4 derives inequalities of partitioned positive semidefinite matrices using Schur complements, while Sections 6.5 and 6.6 investigate the Hadamard product and Kronecker product and related matrix inequalities. Finally, Section 6.7 shows matrix inequalities of the Cauchy-Schwarz type.


Diagonal Entry Positive Semidefinite Kronecker Product Positive Definite Matrix Hermitian Matrix 
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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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