Criteria for invertibility of diagonally dominant matrices
type: Item
instance of: scholarly article
title: Criteria for invertibility of diagonally dominant matrices
zbMATH Open document ID: 0818.15004
DOI: 10.1016/0024-3795(93)00072-8
author: F. O. Farid
published in: Linear Algebra and its Applications
publication date: 1995-04-04T00:00:00Z
review text: The author develops some basic properties of finite diagonally dominant matrices. These properties are used to establish a necessary and sufficient condition for a finite diagonally dominant matrix with nonzero diagonal entries to be singular. This condition relates the nonstrict diagonally dominant rows of the matrix to the difference between the principal arguments of the nonzero entries along each column in these rows. The infinite-dimensional case is also studied, where a sufficient condition for the invertibility of the matrix operator in the sequence space \(c_ 0\) defined by a diagonally dominant infinite matrix \(A\) with nonzero diagonal entries is introduced. This sufficient condition improves some of the earlier results. When the sequence space is \(l_ p\), \(p \in [1, \infty)\), a necessary and sufficient condition for the matrix operator in \(l_ p\) defined by the matrix \(A\) to have a bounded inverse on \(l_ p\) is established.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 47B37
zbMATH DE Number: 740254
zbMATH Keywords: operators on sequence spaces
zbMATH Keywords: diagonally dominant matrices
zbMATH Keywords: invertibility
zbMATH Keywords: matrix operator
zbMATH Keywords: infinite matrix
reviewed by: Ali-Akbar Jafarian
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)00072-8
OpenAlex ID: W2055146237
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description: scientific article; zbMATH DE number 740254