Other Properties
Sinkhorn's theorem states that any matrix with strictly positive entries can be made doubly stochastic by pre- and post-multiplication by diagonal matrices.
For, all bistochastic matrices are unistochastic and orthostochastic, but for larger it is not the case.
Van der Waerden conjectured that the minimum permanent among all n × n doubly stochastic matrices is, achieved by the matrix for which all entries are equal to . Proofs of this conjecture were published in 1980 by B. Gyires and in 1981 by G. P. Egorychev and D. I. Falikman; for this work, Egorychev and Falikman won the Fulkerson Prize in 1982.
Read more about this topic: Doubly Stochastic Matrix
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