Combinatorial Matrix Theory

This group gathers theorems about matrices whose entries are counted, scaled, or arranged to encode combinatorial structure, especially nonnegative and doubly stochastic matrices and the permanent. It covers Sinkhorn's theorem, which states that every square matrix with positive entries can be written in a certain standard form, and related results about doubly stochastic matrices and permutations, such as the Birkhoff-von Neumann theorem and the Bregman-Minc inequality on permanents. General results of linear algebra with no combinatorial content belong with Linear Algebra and Matrix Theory under Algebra.