Positive semidefinite rank
Author(s)Gouveia, João; Robinson, Richard Z.; Thomas, Rekha R.; Parrilo, Pablo A; Fawzi, Hamza
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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.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Springer Berlin Heidelberg
Fawzi, Hamza et al. “Positive Semidefinite Rank.” Mathematical Programming 153.1 (2015): 133–177.
Author's final manuscript