Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/44190
Title: | Polytopes of Minimum Positive Semidefinite Rank | Authors: | Gouveia, João Robinson, Richard Z. Thomas, Rekha R. |
Issue Date: | 2013 | Publisher: | Springer | Project: | PEst-C/MAT/UI0324/2011 | Serial title, monograph or event: | Discrete & Computational Geometry | Volume: | 50 | Issue: | 3 | Abstract: | The positive semidefinite (psd) rank of a polytope is the smallest k for which the cone of 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 in dimensions two and three. | URI: | https://hdl.handle.net/10316/44190 | DOI: | 10.1007/s00454-013-9533-x 10.1007/s00454-013-9533-x |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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revisedGRT.pdf | 357.6 kB | Adobe PDF | View/Open |
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