Majorization polytopes
For two real matrices \(A\) and \(B\) with \(m\) rows, \(A\) majorizes \(B\), written \(A\succ B\), if there is a row-stochastic matrix \(X\) with \(AX=B\), and the associated majorization polytope \({\mathcal M}(A\succ B)\) is the set of row-stochastic matrices \(X\) such that \(AX=B\). The paper studies matrix majorization polytopes and reveals some properties of \({\mathcal M} (A\succ B)\) under some assumptions on \(A\) and \(B\), say, some generalizations of some properties for vector majorization. Relations to transportation polytopes and network flow theory are discussed. A complete description of the vertices of majorization polytopes is presented for some special cases.
scientific article; zbMATH DE number 1400203