Column ranks and their preservers over nonnegative real matrices.
type: Item
instance of: scholarly article
title: Column ranks and their preservers over nonnegative real matrices.
zbMATH Open document ID: 1070.15001
author: Xianqiang Yang
published in: Linear Algebra and its Applications
publication date: 2005-04-21T00:00:00Z
review text: The column rank of a matrix over the nonnegative reals is the least cardinality of the set of columns which span all columns over the nonnegative reals; the rank (also known as factor rank, Boolean rank, Schein rank, Barvinok rank) is the least \(k\) such that the given matrix is a product of \(m\times k\) and \(k\times n\) matrices. The authors determine those sizes of matrices for which the rank necessarily equals the column rank, and characterize linear operators which preserve the rank, and those which preserve the column rank, in various settings over the nonnegative reals.
Mathematics Subject Classification ID: 15A03
Mathematics Subject Classification ID: 15A04
zbMATH DE Number: 2160177
zbMATH Keywords: column rank
zbMATH Keywords: linear operator
zbMATH Keywords: \((U,V)\)-operator
zbMATH Keywords: dominate
zbMATH Keywords: left-nonsingular
zbMATH Keywords: right-nonsingular
zbMATH Keywords: factor rank
zbMATH Keywords: Boolean rank
zbMATH Keywords: Schein rank
zbMATH Keywords: Barvinok rank
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
full work available at URL: j.laa.2004.04.022
OpenAlex ID: W2040995622
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cites work: Linear Operators That Preserve Column Rank of Boolean Matrices
cites work: Spanning column ranks and their preservers of nonnegative matrices
Wikidata QID: Q57702701
DOI: 10.1016/J.LAA.2004.04.022
description: scientific article; zbMATH DE number 2160177