70 citations · 86 across the 5 of their papers we have counts for
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Positive semidefinite rank
Hamza Fawzi, João Gouveia, Pablo A. Parrilo +2
Let M be a p-by-q matrix with nonnegative entries. The positive semidefinite rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite matrices $A_…
Rational and real positive semidefinite rank can be different
João Gouveia, Hamza Fawzi, Richard Z. Robinson
Given a nonnegative matrix M with rational entries, we consider two quantities: the usual positive semidefinite (psd) rank, where the matrix is factored through the cone of real sy…
Worst-Case Results For Positive Semidefinite Rank
João Gouveia, Richard Z. Robinson, Rekha R. Thomas
This paper presents various worst-case results on the positive semidefinite (psd) rank of a nonnegative matrix, primarily in the context of polytopes. We prove that the psd rank of…
Which Nonnegative Matrices Are Slack Matrices?
João Gouveia, Roland Grappe, Volker Kaibel +3
In this paper we characterize the slack matrices of cones and polytopes among all nonnegative matrices. This leads to an algorithm for deciding whether a given matrix is a slack ma…
Polytopes of Minimum Positive Semidefinite Rank
João Gouveia, Richard Z. Robinson, Rekha R. Thomas
The positive semidefinite (psd) rank of a polytope is the smallest for which the cone of real symmetric psd matrices admits an affine slice that projects onto the…