Birkhoff-von Neumann Theorem for Multistochastic Tensors

Lu Bin Cui*, Wen Li, Michael K. Ng

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

27 Citations (Scopus)
36 Downloads (Pure)


In this paper, we study the Birkhoff-von Neumann theorem for a class of multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multistochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly stochastic matrices are just permutation matrices. However, we find that extreme points in the set of multistochastic tensors are not just permutation tensors. We provide the other types of tensors contained in the set of extreme points.

Original languageEnglish
Pages (from-to)956-973
Number of pages18
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
Publication statusPublished - 17 Jul 2014

Scopus Subject Areas

  • Analysis

User-Defined Keywords

  • Doubly stochastic matrices
  • Multistochastic tensors
  • Permanent
  • Permutation tensors


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