Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\)
type: Item
instance of: scholarly article
title: Representation and approximation of the outer inverse \(A_{T,S}^{(2)}\) of a matrix \(A\)
zbMATH Open document ID: 0957.15002
DOI: 10.1016/S0024-3795(99)00269-4
author: Xin Chen
author: Yong-Lin Chen
published in: Linear Algebra and its Applications
publication date: 2000-05-11T00:00:00Z
review text: The authors establish a basic representation and a representation theorem for the outer inverse \(A^{(2)}_{T,S}\) of a matrix \(A\), which is the matrix \(X\) satisfying \[ XAX=X,\;R(X)=T\text{ and }N(X)=S. \] Several specific representations and iterative methods for \(A^{(2)}_{T,S}\) are given. The paper shows that this representation includes many of the traditional generalized inverses and outer inverses, and the relation of the results to these outer inverses will be explored.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 65F20
zbMATH DE Number: 1446345
zbMATH Keywords: generalized inverses
zbMATH Keywords: limit representation
zbMATH Keywords: Neumann expansion
zbMATH Keywords: representation
zbMATH Keywords: outer inverse
zbMATH Keywords: iterative methods
reviewed by: Rodica Covaci
MaRDI profile type: Publication
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full work available at URL: s0024-3795(99)00269-4
OpenAlex ID: W2055610189
Wikidata QID: Q126298275
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description: scientific article; zbMATH DE number 1446345