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- Title
Polytopes of Minimum Positive Semidefinite Rank.
- Authors
Gouveia, João; Robinson, Richard Z.; Thomas, Rekha R.
- Abstract
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 in dimensions two and three.
- Subjects
POLYTOPES; SEMIDEFINITE programming; MATRICES (Mathematics); MATHEMATICAL symmetry; HADAMARD matrices; SQUARE root; DIMENSION theory (Topology)
- Publication
Discrete & Computational Geometry, 2013, Vol 50, Issue 3, p679
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-013-9533-x