Positive Semidefinite Matrices

Abdo Y. Alfakih
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Abdo Y. Alfakih: University of Windsor, Department of Mathematics and Statistics

Chapter Chapter 2 in Euclidean Distance Matrices and Their Applications in Rigidity Theory, 2018, pp 29-50 from Springer

Abstract: 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.

Keywords: Face Reduction; Spectrahedron; Relint; Minimal Face; Full Column Rank Matrix (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-97846-8_2

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DOI: 10.1007/978-3-319-97846-8_2

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