The phaseless rank of a nonnegative matrix M is defined to be the least k for which there exists a complex matrix N such that |N| = M, entrywise speaking. In optimization terms, it is the solution to the rank minimization of a matrix under phase uncertainty on the entries. This concept has a strong connection with some algebraic objects, called amoebas. An algebraic amoeba is the image of an algebraic variety under the absolute value map. In this talk we state some results related to phaseless rank and explore its connection with amoebas. (*) António Goucha is a PhD student of the Joint PhD Program UC|UP, working at the University of Coimbra, in Optimization, under the supervision of Professor João Gouveia.
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