Inverse \(M\)-matrix inequalities and generalized ultrametric matrices
type: Item
instance of: scholarly article
title: Inverse \(M\)-matrix inequalities and generalized ultrametric matrices
zbMATH Open document ID: 0824.15020
DOI: 10.1016/0024-3795(94)00077-Q
author: M. Neumann
author: Hans Schneider
author: M. Tsatsomeros
author: J. J. McDonald
published in: Linear Algebra and its Applications
publication date: 1995-11-14T00:00:00Z
review text: The authors introduce a class of matrices called generalized ultrametric matrices. That class is defined in terms of triangles in the weighted graph of the matrix, and it contains the ultrametric matrices as well as some unsymmetric matrices. The authors show that a generalized ultrametric matrix is the inverse of a row diagonally dominant \(M\)-matrix if and only if it contains no zero row and no two of its rows are identical. Inequalities and conditions for equality among the entries of the inverse of a row diagonally dominant \(M\)-matrix are also presented. Some of these inequalities and conditions for equality generalize results of Stieltjes on inverses of symmetric diagonally dominant \(M\)-matrices.
reviewed by: Silvestru Sever Dragomir
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 769032
zbMATH Keywords: inverse \(M\)-matrix inequalities
zbMATH Keywords: generalized ultrametric matrices
zbMATH Keywords: weighted graph
zbMATH Keywords: inverse
zbMATH Keywords: diagonally dominant \(M\)-matrix
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 769032