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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…
Sums of Squares on the Hypercube
Grigoriy Blekherman, João Gouveia, James Pfeiffer
Let X be a finite set of points in R^n. A polynomial p nonnegative on X can be written as a sum of squares of rational functions modulo the vanishing ideal I(X). From the point of…