70 citations · 86 across the 5 of their papers we have counts for
7 papers
Positive semidefinite rank and nested spectrahedra
Kaie Kubjas, Elina Robeva, Richard Z. Robinson
The set of matrices of given positive semidefinite rank is semialgebraic. In this paper we study the geometry of this set, and in small cases we describe its boundary. For general…
Four Dimensional Polytopes of Minimum Positive Semidefinite Rank
João Gouveia, Kanstanstin Pashkovich, Richard Z. Robinson +1
The positive semidefinite (psd) rank of a polytope is the size of the smallest psd cone that admits an affine slice that projects linearly onto the polytope. The psd rank of a d-po…
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…