Positive Semidefinite Matrices

  • Abdo Y. Alfakih


Positive semidefinite (PSD) and positive definite (PD) matrices are closely connected with Euclidean distance matrices. Accordingly, they play a central role in this monograph. This chapter reviews some of the basic results concerning these matrices. Among the topics discussed are various characterizations of PSD and PD matrices, theorems of the alternative for the semidefinite cone, the facial structures of the semidefinite cone and spectrahedra, as well as the Borwein–Wolkowicz facial reduction scheme.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Abdo Y. Alfakih
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of WindsorWindsorCanada

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