Determinantal representation of weighted generalized inverses
type: Item
instance of: scholarly article
title: Determinantal representation of weighted generalized inverses
zbMATH Open document ID: 1160.15006
author: Xiaoji Liu
author: Yaoming Yu
author: Hongxing Wang
published in: Applied Mathematics and Computation
publication date: 2009-03-10T00:00:00Z
review text: \textit{D.~W. Robinson} [Linear Algebra Appl. 411, 254--276 (2005; Zbl 1086.15500)] studied the Moore-Penrose inverse of a matrix in a commutative ring and gave a determinantal formula for the Moore-Penrose inverse. The authors of the present paper introduce some determinantal representations of the weighted generalized inverse by using a result of the paper above. They also present a method for computing minors of the weighted Moore-Penrose inverse and the W-weighted Drazin inverse.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 65F40
zbMATH DE Number: 5527467
zbMATH Keywords: determinantal representation
zbMATH Keywords: minor
zbMATH Keywords: weighted Moore-Penrose inverse
zbMATH Keywords: W-weighted Drazin inverse
zbMATH Keywords: commutative ring
MaRDI profile type: Publication
full work available at URL: j.amc.2008.12.030
OpenAlex ID: W2072703253
cites work: Generalized inverses over integral domains
cites work: A volume associated with \(m{\times}n\) matrices
cites work: Q4061081
cites work: Three results in connection with inverse matrices
cites work: On generalized inverses of matrices over integral domains
cites work: Representations for the Generalized Inverse of Sums of Matrices
cites work: Generalizing Cramer's Rule: Solving Uniformly Linear Systems of Equations
cites work: Matrix Analysis
cites work: Analogs of the adjoint matrix for generalized inverses and corresponding Cramer rules
cites work: The generalized Moore-Penrose inverse
cites work: Generalized inverses over integral domains. II: Group inverses and Drazin inverses
cites work: Reflexive generalized inverses and their minors*
cites work: Minors of the Moore-Penrose inverse
cites work: The classical adjoint
cites work: A Short Proof of Cramer's Rule
cites work: Determinantal representation of \(\{i,j,k\}\) inverses and solution to linear systems
cites work: Q4258631
cites work: Full-rank and determinantal representation of the Drazin inverse
cites work: Q4542909
cites work: Q4435199
cites work: Upper Perturbation Bounds of Weighted Projections, Weighted and Constrained Least Squares Problems
cites work: A characterization for the \(W\)-weighted Drazin inverse and a Cramer rule for the \(W\)-weighted Drazin inverse solution
cites work: Determinantal representation of the generalized inverse\bi A_{T,S}^{(2)}over integral domains and its applications
DOI: 10.1016/J.AMC.2008.12.030
description: scientific article; zbMATH DE number 5527467