Majorization polytopes
type: Item
instance of: scholarly article
title: Majorization polytopes
zbMATH Open document ID: 0943.15012
DOI: 10.1016/S0024-3795(99)00148-2
author: Geir Dahl
published in: Linear Algebra and its Applications
publication date: 2000-08-30T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 15B51
Mathematics Subject Classification ID: 52B12
Mathematics Subject Classification ID: 90B06
zbMATH DE Number: 1400203
zbMATH Keywords: matrix majorization
zbMATH Keywords: majorization polytope
zbMATH Keywords: majorization polytope vertices
zbMATH Keywords: network flow theory
zbMATH Keywords: row-stochastic matrix
zbMATH Keywords: transportation polytope
zbMATH Keywords: vector majorization
reviewed by: Huang Wenxue
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1400203