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math.AG2021
The phase rank of a matrix
António Pedro Goucha, João Gouveia
In this paper, we introduce and study the notion of phase rank. Given a matrix filled with phases, i.e., with complex entries of modulus , its phase rank is the smallest possibl…
math.AG2019
The phaseless rank of a matrix
António Pedro Goucha, João Gouveia
We consider the problem of finding the smallest rank of a complex matrix whose absolute values of the entries are given. We call this minimum the phaseless rank of the matrix of th…
math.AG2014★ 1 cited
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…