The computation and perturbation analysis for weighted group inverse of rectangular matrices
type: Item
instance of: scholarly article
title: The computation and perturbation analysis for weighted group inverse of rectangular matrices
zbMATH Open document ID: 1178.65039
author: Xingping Sheng
author: Guoliang Chen
published in: Journal of Applied Mathematics and Computing
publication date: 2009-11-09T00:00:00Z
review text: The weighted group inverse \(A^{\#}_W\) of a matrix \(A \in \mathbb{C}^{m\times n}\) with respect to a matrix \(W \in \mathbb{C}^{n\times m}\) was defined by \textit{J. Cen} [Math. Numer. Sin. 29, No.~1, 39--48 (2007; Zbl 1121.15303)] as the solution \(X\in \mathbb{C}^{n \times m}\) of the matrix equations \(AWXWA= A, XWAWX = X, AWX=XWA\). The present authors study algebraic perturbations and analytical perturbations of the weighted group inverse \(A^{\#}_W\), and give a new representation based on Gauss elimination. They use this representation to compute the weighted group inverse.
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 65F20
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5627251
zbMATH Keywords: rectangular matrices
zbMATH Keywords: weighted group inverse
zbMATH Keywords: algebraic perturbation
zbMATH Keywords: analytical perturbation
zbMATH Keywords: representation
zbMATH Keywords: matrix equations
zbMATH Keywords: Gauss elimination
MaRDI profile type: Publication
full work available at URL: s12190-008-0189-2
OpenAlex ID: W2011077345
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DOI: 10.1007/S12190-008-0189-2
description: scientific article; zbMATH DE number 5627251