Stability of acyclic matrices
type: Item
instance of: scholarly article
title: Stability of acyclic matrices
zbMATH Open document ID: 0588.15012
DOI: 10.1016/0024-3795(86)90238-7
author: Daniel Hershkowitz
published in: Linear Algebra and its Applications
publication date: 1986-01-01T00:00:00Z
review text: The nondirect graph G(A) of an \(n\times n\)-matrix A is defined as a set of vertices \(\{\) 1,2,...,n\(\}\) and (i,j) is an edge of G(A) iff \(a_{ij}\neq 0\) or \(a_{ji}\neq 0\) (i\(\neq j)\). A matrix is called acyclic if its nondirected graph contains no cycles. The author finds necessary and sufficient conditions for an acyclic matrix A whose principal minors are nonnegative to be stable. The conditions are expressed in terms of G(A). Some conditions related to additive D-stable acyclic matrices are also given (A is called additive D-stable if \(D+\) is stable for every nonnegative diagonal matrix D).
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 3944043
zbMATH Keywords: nondirect graph
zbMATH Keywords: acyclic matrix
zbMATH Keywords: additive D-stable
reviewed by: Boris Raykhshteyn
MaRDI profile type: Publication
full work available at URL: 0024-3795(86)90238-7
OpenAlex ID: W1971698672
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description: scientific article; zbMATH DE number 3944043