On relationships between several classes of Z-matrices, M-matrices and nonnegative matrices
type: Item
instance of: scholarly article
title: On relationships between several classes of Z-matrices, M-matrices and nonnegative matrices
zbMATH Open document ID: 1124.15019
author: Reinhard Nabben
published in: Linear Algebra and its Applications
publication date: 2007-03-09T00:00:00Z
review text: The author establishes relationships between several different classes of matrices. The classes of Z- and M-matrices are among the best-known, and these matrices have numerous important applications. Other types are ZMA- and MMA-matrices: real matrices all of whose positive powers are irreducible Z- and M-matrices, respectively. There are also Soules-matrices, strictly ultrametric matrices or SUMs, shifted SUMs, and two new classes introduced by the author: ZSUMs and MSUMs. Many different relationships, based on the concept of diagonal congruence, are established between these classes.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5132608
zbMATH Keywords: MMA-matrices
zbMATH Keywords: ZMA-matrices
zbMATH Keywords: Soules matrices
zbMATH Keywords: strictly ultrametric matrices
zbMATH Keywords: shifted sums
zbMATH Keywords: diagonal congruence
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: j.laa.2006.10.015
OpenAlex ID: W1980324327
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DOI: 10.1016/J.LAA.2006.10.015
description: scientific article; zbMATH DE number 5132608