Generalized inverse \(A^{(2)}_{T,S}\) and a rank equation
type: Item
instance of: scholarly article
title: Generalized inverse \(A^{(2)}_{T,S}\) and a rank equation
zbMATH Open document ID: 1057.15008
DOI: 10.1016/S0096-3003(03)00786-0
author: Bing Zheng
author: R. B. Bapat
published in: Applied Mathematics and Computation
publication date: 2004-10-13T00:00:00Z
review text: The paper establishes the connection between the matrices \(A\in \mathbb{R} ^{m\times n},B\in \mathbb{R} ^{n\times n},C\in \mathbb{R} ^{m\times m}\) in order \(X=A_{T,S}^{(2)}\) (the outer inverse of \(A\) with prescribed range \(T\) and null space \(S\)) be the solution of the rank equation : rank\(\left( \begin{smallmatrix} A & B \\ C & X \end{smallmatrix} \right) \)= rank\((A) \). As special cases, the corresponding results for the Moore-Penrose inverse \(A^{\dag }\), the weighted Moore-Penrose inverse \(A_{M,N}^{+}\), the Drazin inverse \(A^{D}\) and the group inverse \(A^{\#}\) are also derived.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A03
zbMATH DE Number: 2107393
zbMATH Keywords: rank equation
zbMATH Keywords: characterization
zbMATH Keywords: generalized inverse
zbMATH Keywords: matrix decomposition
zbMATH Keywords: outer inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: Drazin inverse
zbMATH Keywords: group inverse
reviewed by: Nicholas Karampetakis
MaRDI profile type: Publication
Wikidata QID: Q56660709
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description: scientific article; zbMATH DE number 2107393