Positive semidefinite rank

Author(s)
Gouveia, João; Robinson, Richard Z.; Thomas, Rekha R.; Parrilo, Pablo A; Fawzi, Hamza
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Abstract
Let M∈R[superscript p×q] be a nonnegative matrix. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices A[subscript i],B[subscript j] of size k×k such that M[subscript ij]=trace(A[subscript i]B[subscript j]). The psd rank has many appealing geometric interpretations, including semidefinite representations of polyhedra and information-theoretic applications. In this paper we develop and survey the main mathematical properties of psd rank, including its geometry, relationships with other rank notions, and computational and algorithmic aspects.
Date issued
2015-07
URI
http://hdl.handle.net/1721.1/106864
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
Mathematical Programming
Publisher
Springer Berlin Heidelberg
Citation
Fawzi, Hamza et al. “Positive Semidefinite Rank.” Mathematical Programming 153.1 (2015): 133–177.
Version: Author's final manuscript
ISSN
0025-5610
1436-4646
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