Majorization polytopes

Abstract

We study polytopes related to the concept of matrix majorization: for two real matrices A and B having m rows we say that A majorizes B if there is a row-stochastic matrix X with AX = B . In that case we write A ≻ B and the associated majorization polytope M( A ≻ B ) is the set of row stochastic matrices X such that AX = B . We investigate some properties of M( A ≻ B ) and obtain e.g., generalizations of some results known for vector majorization. Relations to transportation polytopes and network flow theory are discussed. A complete description of the vertices of majorization polytopes is found for some special cases.