Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 7, Number 3 (2016), 386-393.
Polytopes of stochastic tensors
Considering stochastic tensors (i.e., nonnegative hypermatrices in which every sum over one index , , or , is 1), we study the polytope () of all these tensors, the convex set () of all tensors in with some positive diagonals, and the polytope () generated by the permutation tensors. We show that is almost the same as except for some boundary points. We also present an upper bound for the number of vertices of .
Ann. Funct. Anal., Volume 7, Number 3 (2016), 386-393.
Received: 18 September 2015
Accepted: 26 November 2015
First available in Project Euclid: 19 May 2016
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Chang, Haixia; Paksoy, Vehbi E.; Zhang, Fuzhen. Polytopes of stochastic tensors. Ann. Funct. Anal. 7 (2016), no. 3, 386--393. doi:10.1215/20088752-3605195. https://projecteuclid.org/euclid.afa/1463684084