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The Moore-Penrose inverse of a factorization

Bibliographic Details
Main Author: Patrício, Pedro
Publication Date: 2003
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: https://hdl.handle.net/1822/3237
Summary: In this paper, we consider the product of matrices $PAQ$, where $A$ is von Neumann regular and there exist $P^{\prime }$ and $Q^{\prime }$ such that $P^{\prime }PA=A=AQQ^{\prime }$. We give necessary and sufficient conditions in order to $PAQ$ be Moore-Penrose invertible, extending known characterizations. Finally, an application is given to matrices over separative regular rings.
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spelling The Moore-Penrose inverse of a factorizationMatrices over ringsVon Neumann regularityMoore-Penrose invertibilityFactorizationSeparative regular ringsScience & TechnologyIn this paper, we consider the product of matrices $PAQ$, where $A$ is von Neumann regular and there exist $P^{\prime }$ and $Q^{\prime }$ such that $P^{\prime }PA=A=AQQ^{\prime }$. We give necessary and sufficient conditions in order to $PAQ$ be Moore-Penrose invertible, extending known characterizations. Finally, an application is given to matrices over separative regular rings.Fundação para a Ciência e a Tecnologia (FCT).Programa de Desenvolvimento Educativo para Portugal III (PRODEP III) - proj. 5.3/N/189.007/00).Elsevier B.V.Universidade do MinhoPatrício, Pedro20032003-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/1822/3237eng0024-379510.1016/S0024-3795(03)00391-4info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-04-12T03:50:56Zoai:repositorium.sdum.uminho.pt:1822/3237Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T14:40:49.302369Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv The Moore-Penrose inverse of a factorization
title The Moore-Penrose inverse of a factorization
spellingShingle The Moore-Penrose inverse of a factorization
Patrício, Pedro
Matrices over rings
Von Neumann regularity
Moore-Penrose invertibility
Factorization
Separative regular rings
Science & Technology
title_short The Moore-Penrose inverse of a factorization
title_full The Moore-Penrose inverse of a factorization
title_fullStr The Moore-Penrose inverse of a factorization
title_full_unstemmed The Moore-Penrose inverse of a factorization
title_sort The Moore-Penrose inverse of a factorization
author Patrício, Pedro
author_facet Patrício, Pedro
author_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Patrício, Pedro
dc.subject.por.fl_str_mv Matrices over rings
Von Neumann regularity
Moore-Penrose invertibility
Factorization
Separative regular rings
Science & Technology
topic Matrices over rings
Von Neumann regularity
Moore-Penrose invertibility
Factorization
Separative regular rings
Science & Technology
description In this paper, we consider the product of matrices $PAQ$, where $A$ is von Neumann regular and there exist $P^{\prime }$ and $Q^{\prime }$ such that $P^{\prime }PA=A=AQQ^{\prime }$. We give necessary and sufficient conditions in order to $PAQ$ be Moore-Penrose invertible, extending known characterizations. Finally, an application is given to matrices over separative regular rings.
publishDate 2003
dc.date.none.fl_str_mv 2003
2003-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://hdl.handle.net/1822/3237
url https://hdl.handle.net/1822/3237
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0024-3795
10.1016/S0024-3795(03)00391-4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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