Double Soules pairs and matching Soules bases
type: Item
instance of: scholarly article
title: Double Soules pairs and matching Soules bases
zbMATH Open document ID: 1126.15026
author: N. E. Zubov
published in: Linear Algebra and its Applications
publication date: 2007-03-09T00:00:00Z
review text: This paper deals with double Soules pairs and bases. A Soules basis matrix is an orthogonal matrix \(R\) with a positive first column, such that \(R\Lambda R^T\) is nonnegative for every nonnegative diagonal matrix \(\Lambda\) with nonincreasing diagonal elements [\textit{G. W. Soules}, Linear Multilinear Algebra 13, 241--251 (1983; Zbl 0516.15013)]. In the same paper, for a positive unit vector, a Soules basis matrix with that vector as its first column is constructed. Later, in \textit{L. Elsner, R. Nabben} and \textit{M. Neumann} [Linear Algebra Appl. 271, 323--343 (1998; Zbl 0891.15019)] described all \(n\times n\) matrices of this type and considered Soules matrices. Afterwards, \textit{M. Q. Chen, L. Han} and \textit{M. Neumann} [Linear Algebra Appl. 416, No.~1, 88--110 (2006; Zbl 1109.15015)] introduced the notion of a double Soules pair, providing an algorithm for generating such pairs of matrices. In the current paper the authors show how to construct all double Soules pairs and properties of the nonnegative matrices generated by them are studied. In addition, the authors consider a second generalization, namely a pair of matching Soules bases. Characterizations are given, and properties of the generated generalized inverses are discussed.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 5132599
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: \(M\)-matrices
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: generalized inverses
zbMATH Keywords: algorithm
reviewed by: J. Rafael Sendra
MaRDI profile type: Publication
full work available at URL: j.laa.2006.08.016
OpenAlex ID: W2147592621
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DOI: 10.1016/J.LAA.2006.08.016
description: scientific article; zbMATH DE number 5132599