Lyapunov diagonal semistability of real H-matrices
type: Item
instance of: scholarly article
title: Lyapunov diagonal semistability of real H-matrices
zbMATH Open document ID: 0577.15015
DOI: 10.1016/0024-3795(85)90241-1
author: Daniel Hershkowitz
author: Hans Schneider
published in: Linear Algebra and its Applications
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: Let \(A\) be an \(n\times n\) matrix and define the comparison matrix \(B=M(A)\) by \(b_{jj}= \vert a_{jj}\vert\) and \(b_{jk}= - \vert a_{jk}\vert\), \(j\neq k\). Then \(A\) is an H-matrix if \(M(A)\) is an M-matrix. The authors characterize diagonally stable real H-matrices and those real H-matrices which are diagonally semistable but not diagonally stable. The results are applied to a study of the numerical abscissa of real matrices. The work is given in terms of properties of principal submatrices and uses results on determinants due to A. Ostrowski.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 3922880
zbMATH Keywords: Lyapunov diagonal stability
zbMATH Keywords: irreducibility
zbMATH Keywords: Lyapunov scaling
zbMATH Keywords: factor
zbMATH Keywords: comparison matrix
zbMATH Keywords: H-matrix
zbMATH Keywords: M-matrix
reviewed by: George Phillip Barker
MaRDI profile type: Publication
OpenAlex ID: W2101521550
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description: scientific article; zbMATH DE number 3922880