On weak r-monotonicity
type: Item
instance of: scholarly article
title: On weak r-monotonicity
zbMATH Open document ID: 0606.15013
DOI: 10.1016/0024-3795(87)90295-3
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: A real square matrix A is monotone iff Ax\(\geq 0\) implies \(x\geq 0\) (where the inequalities are entrywise). More generally, a real \(m\times n\) matrix A of order r is weak r-monotone if A has a monotone submatrix of order r. A real \(m\times n\) matrix A is \(\{\) \(1\}\)-monotone iff there is a nonnegative matrix X which satisfies the equation \(AXA=A\). These two generalizations of monotonicity are not equivalent in general. The author obtains a condition under which they are.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 3979272
zbMATH Keywords: weak r-monotonicity
zbMATH Keywords: \(\{\) 1\(\}\)-monotonicity
author: Hans Joachim Werner
reviewed by: George Phillip Barker
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90295-3
OpenAlex ID: W1979197520
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description: scientific article; zbMATH DE number 3979272