# Positive semidefinite rank

@article{Fawzi2014PositiveSR,
title={Positive semidefinite rank},
author={Hamza Fawzi and Jo{\~a}o Gouveia and Pablo A. Parrilo and Richard Z. Robinson and Rekha R. Thomas},
journal={Mathematical Programming},
year={2014},
volume={153},
pages={133-177}
}
• Published 15 July 2014
• Mathematics
• Mathematical Programming
Let $$M \in \mathbb {R}^{p \times q}$$M∈Rp×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 $$A_i, B_j$$Ai,Bj of size $$k \times k$$k×k such that $$M_{ij} = {{\mathrm{trace}}}(A_i B_j)$$Mij=trace(AiBj). 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…

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