On the class of \(\{1,2,4\}\) inverses as solution of a linear problem
type: Item
instance of: scholarly article
title: On the class of \(\{1,2,4\}\) inverses as solution of a linear problem
zbMATH Open document ID: 0926.15004
author: M. E. Díaz Lozano
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 1999-12-05T00:00:00Z
review text: Let \(A\) be an \(m\times n\) real matrix. The paper works out a characterization of those \(n\times m\) matrices \(X\) that satisfy the three conditions (1) \(AXA=A\); (2) \(XAX=X\); and (4) \((XA)^T= XA\). By ignoring condition (3) (i.e., \((AX)^T= AX\)), which in the presence of the other three conditions would force \(X\) to be the usual (and unique!) Moore-Penrose generalized inverse \(A^+\) of \(A\), the author is able to show that the matrices \(X\) are in bijective correspondence with the set of vector space complements of the column space of \(A\).
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1240996
zbMATH Keywords: \(\{1,2,4\}\) inverses
zbMATH Keywords: generalized inverse
zbMATH Keywords: vector space complements
reviewed by: Stanley E. Payne
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1240996