Nonnegative alternating circulants leading to \(M\)-matrix group inverses
type: Item
instance of: scholarly article
title: Nonnegative alternating circulants leading to \(M\)-matrix group inverses
zbMATH Open document ID: 0841.15005
DOI: 10.1016/0024-3795(94)00055-7
author: Yonghong Chen
author: M. Neumann
author: S. J. Kirkland
published in: Linear Algebra and its Applications
publication date: 1996-07-24T00:00:00Z
review text: Let \(\mathcal C\) denote the set of all irreducible nonnegative alternating circulant matrices, i.e. all matrices \(A= \sum^{n- 1}_{i= 0} \alpha_i P^i\), when \(P\) is an \(n\)th order cyclic permutation matrix, where \(\alpha_i> 0\) and \(\alpha_i= \alpha_j\) for \(i= j\pmod 2\). Those matrices \(B\) in \(\mathcal C\) are characterized for which the group inverse \((rI- B)^{\neq}\), where \(r= \rho(B)\), is also an \(M\)-matrix. For those matrices \(\rho(B)\) is a concave function of the off-diagonal entries.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 841739
zbMATH Keywords: concavity of spectral radius
zbMATH Keywords: irreducible nonnegative alternating circulant matrices
zbMATH Keywords: permutation matrix
zbMATH Keywords: group inverse
zbMATH Keywords: \(M\)-matrix
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)00055-7
OpenAlex ID: W2089371084
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description: scientific article; zbMATH DE number 841739