Proof of a conjecture concerning the Hadamard powers of inverse \(M\)-matrices
type: Item
instance of: scholarly article
title: Proof of a conjecture concerning the Hadamard powers of inverse \(M\)-matrices
zbMATH Open document ID: 1117.15021
author: S.-C. Chen
published in: Linear Algebra and its Applications
publication date: 2007-04-10T00:00:00Z
review text: Let \(A\) be a real \(n\times n\) matrix. Assume that (i) all entries of \(A\) are nonnegative; and (ii) \(A^{-1}\) exists and all its off-diagonal entries are nonnegative (briefly: \(A\) is an inverse \(M\)-matrix). Let \(A^{(r)}\) denote the matrix obtained from \(A\) by raising each entry to the \(r\)th power (\(r>1\)). The author shows that \(A^{(r)}\) is also an inverse \(M\)-matrix. This verifies a conjecture of \textit{B. Wang, X. Zhang} and \textit{F. Zhang} [Linear Algebra Appl. 305, No. 1--3, 23--31 (2000; Zbl 0948.15004)].
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5141627
zbMATH Keywords: Hadamard product
zbMATH Keywords: \(M\)-matrix
zbMATH Keywords: inverse \(M\)-matrix
MaRDI profile type: Publication
full work available at URL: j.laa.2006.11.005
OpenAlex ID: W1992278177
Wikidata QID: Q123333959
cites work: On the Hadamard product of inverse \(M\)-matrices
cites work: A conjecture concerning the Hadamard product of inverses of \(M\)-matrices
cites work: A property concerning the Hadamard powers of inverse \(M\)-matrices.
cites work: Inverse M-matrices
cites work: Almost principal minors of inverse \(M\)-matrices
cites work: The inverse M-matrix problem
DOI: 10.1016/J.LAA.2006.11.005
description: scientific article; zbMATH DE number 5141627