# Polytopes of Minimum Positive Semidefinite Rank

@article{Gouveia2013PolytopesOM,
title={Polytopes of Minimum Positive Semidefinite Rank},
author={Jo{\~a}o Gouveia and Richard Z. Robinson and Rekha R. Thomas},
journal={Discrete \& Computational Geometry},
year={2013},
volume={50},
pages={679-699}
}
• Published 23 May 2012
• Mathematics
• Discrete & Computational Geometry
The positive semidefinite (psd) rank of a polytope is the smallest $$k$$k for which the cone of $$k \times k$$k×k real symmetric psd matrices admits an affine slice that projects onto the polytope. In this paper we show that the psd rank of a polytope is at least the dimension of the polytope plus one, and we characterize those polytopes whose psd rank equals this lower bound. We give several classes of polytopes that achieve the minimum possible psd rank including a complete characterization…
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