Journal
DISCRETE & COMPUTATIONAL GEOMETRY
Volume 50, Issue 3, Pages 679-699Publisher
SPRINGER
DOI: 10.1007/s00454-013-9533-x
Keywords
Positive semidefinite rank; Polytope; Slack matrix; Hadamard square roots; Cone lift
Categories
Funding
- Centre for Mathematics at the University of Coimbra
- Fundacao para a Ciencia e a Tecnologia through the European Program COMPETE/FEDER
- U.S. National Science Foundation Graduate Research Fellowship [DGE-0718124]
- U.S. National Science Foundation Grant [DMS-1115293]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1115293] Funding Source: National Science Foundation
Ask authors/readers for more resources
The positive semidefinite (psd) rank of a polytope is the smallest for which the cone of 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available
Share Paper
