Positive semidefinite rank
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Author(s)
Gouveia, João
Robinson, Richard Z.
Thomas, Rekha R.
Parrilo, Pablo A
Fawzi, Hamza
Date Issued
July 2015
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10107-015-0922-1
