Article
Polytopes of Stochastic Tensors
Annals of Functional Analysis
Document Type
Article
Publication Date
8-1-2016
Keywords
- Doubly stochastic matrix,
- Extreme point,
- Polytope,
- Stochastic semi-magic cube,
- Stochastic tensor
Disciplines
Abstract
Considering n × n × n stochastic tensors (aijk)(i.e., nonnegative hypermatrices in which every sum over one index i, j, or k, is 1), we study the polytope (Ωn) of all these tensors, the convex set (Ln) of all tensors in Ωn with some positive diagonals, and the polytope (Δn) generated by the permutation tensors. We show that LnLn is almost the same as Ωn except for some boundary points. We also present an upper bound for the number of vertices of Ωn.
DOI
10.1215/20088752-3605195
Citation Information
Haixia Chang, Vehbi Emrah Paksoy and Fuzhen Zhang. "Polytopes of Stochastic Tensors" Annals of Functional Analysis Vol. 7 Iss. 3 (2016) p. 386 - 393 ISSN: 2008-8752 Available at: http://works.bepress.com/fuzhen-zhang/162/
©2016 by the Tusi Mathematical Research Group