Rational and real positive semidefinite rank can be different

João Gouveia; Hamza Fawzi; Richard Z. Robinson

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arXiv · 1404.4864

Rational and real positive semidefinite rank can be different

João Gouveia·Hamza Fawzi·Richard Z. Robinson

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Abstract

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 symmetric psd matrices, and the rational-restricted psd rank, where the matrix factors are required to be rational symmetric psd matrices. It is clear that the rational-restricted psd rank is always an upper bound to the usual psd rank. We show that this inequality may be strict by exhibiting a matrix with psd rank four whose rational-restricted psd rank is strictly greater than four.

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BibTeX RIS

João Gouveia, Hamza Fawzi, Richard Z. Robinson. 2014-04-18. Rational and real positive semidefinite rank can be different. https://arxiv.org/abs/1404.4864

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