Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	The phaseless rank of a matrix
Publication Date:	2019-09-02
Authors:	- António Pedro Neves Goucha - João Gouveia
Abstract:	We consider the problem of minimizing the rank of a complex matrix where the absolute values of the entries are given. We call this minimum the phaseless rank of the matrix of entrywise absolute values. In this paper we study this quantity, extending a classic result of Camion and Hoffman and connecting it to the study of amoebas of determinantal varieties and of semidefinite representations of convex sets. As a consequence, we attain several new results, including a counterexample for a conjecture of Nisse and Sottile on the existence of amoeba bases, and a new upper bound on the complex semidefinite extension complexity of polytopes, dependent only on their number of vertices and facets.
Institution:	DMUC 19-29
Online version:	http://www.mat.uc.pt...prints/eng_2019.html
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