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Positive Semidefinite Matrices

In: Euclidean Distance Matrices and Their Applications in Rigidity Theory

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  • Abdo Y. Alfakih

    (University of Windsor, Department of Mathematics and Statistics)

Abstract

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.

Suggested Citation

  • Abdo Y. Alfakih, 2018. "Positive Semidefinite Matrices," Springer Books, in: Euclidean Distance Matrices and Their Applications in Rigidity Theory, chapter 0, pages 29-50, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-97846-8_2
    DOI: 10.1007/978-3-319-97846-8_2
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