Inverse \(M\)-matrix completions of patterns omitting some diagonal positions
type: Item
instance of: scholarly article
title: Inverse \(M\)-matrix completions of patterns omitting some diagonal positions
zbMATH Open document ID: 0958.15010
DOI: 10.1016/S0024-3795(00)00122-1
author: Leslie Hogben
published in: Linear Algebra and its Applications
publication date: 2000-12-14T00:00:00Z
review text: Let \(N= \{1,\dots, n\}\). The author investigates the following question: Which subsets \(Q\) of \(N\times N\) have the property that whenever \(a_{ij}\) for \((i,j)\in Q\) form a ``partial inverse \(M\)-matrix'' (i.e., \(a_{ij}\geq 0\) and if \(L\times L\subseteq Q\), then the inverse of \(\{a_{ij}:i, j\in L\}\) is an \(M\)-matrix), \(a_{ij}\) can be defined for \((i,j)\not\in Q\) so that the inverse of \(A= [a_{ij}]\) is an \(M\)-matrix?
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1506786
zbMATH Keywords: \(M\)-matrices
zbMATH Keywords: matrix completions
zbMATH Keywords: graph
zbMATH Keywords: inverse M-matrix
zbMATH Keywords: digraph
zbMATH Keywords: pattern
reviewed by: Robert Guralnick
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1506786