The generalized inverses of tensors and an application to linear models

[EN] In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the leastsquares solutions of tensor equations. An algorithm to compute the Moore Penrose inverse of an arbitrary tensor is con...

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Authors: Jin, Hongwei, Bai, Minru, Liu, Xiaoji, Benítez López, Julio|||0000-0002-3222-3036
Format: article
Publication Date:2017
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/103606
Online Access:https://riunet.upv.es/handle/10251/103606
Access Level:Open access
Keyword:Tensors
Generalized inverses
Moore Penrose inverse of tensors
Linear models
MATEMATICA APLICADA
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network_name_str España
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spelling The generalized inverses of tensors and an application to linear modelsJin, HongweiBai, MinruLiu, XiaojiBenítez López, Julio|||0000-0002-3222-3036TensorsGeneralized inversesMoore Penrose inverse of tensorsLinear modelsMATEMATICA APLICADA[EN] In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the leastsquares solutions of tensor equations. An algorithm to compute the Moore Penrose inverse of an arbitrary tensor is constructed. Finally, we apply the obtained results to higher order Gauss Markov theoremThe fourth author was supported by the National Science Foundation of China [grant number 11361009] and Grant from the High level innovation teams and distinguished scholars in Guangxi Universities [grant number 20160001].ElsevierEscuela Técnica Superior de Ingeniería de TelecomunicaciónDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarNational Science Foundation, ChinaRepositorio Institucional de la Universitat Politècnica de València Riunet20172017-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/103606reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengNational Natural Science Foundation of China https://doi.org/10.13039/501100001809 11361009open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1036062026-06-13T07:49:27Z
dc.title.none.fl_str_mv The generalized inverses of tensors and an application to linear models
title The generalized inverses of tensors and an application to linear models
spellingShingle The generalized inverses of tensors and an application to linear models
Jin, Hongwei
Tensors
Generalized inverses
Moore Penrose inverse of tensors
Linear models
MATEMATICA APLICADA
title_short The generalized inverses of tensors and an application to linear models
title_full The generalized inverses of tensors and an application to linear models
title_fullStr The generalized inverses of tensors and an application to linear models
title_full_unstemmed The generalized inverses of tensors and an application to linear models
title_sort The generalized inverses of tensors and an application to linear models
dc.creator.none.fl_str_mv Jin, Hongwei
Bai, Minru
Liu, Xiaoji
Benítez López, Julio|||0000-0002-3222-3036
author Jin, Hongwei
author_facet Jin, Hongwei
Bai, Minru
Liu, Xiaoji
Benítez López, Julio|||0000-0002-3222-3036
author_role author
author2 Bai, Minru
Liu, Xiaoji
Benítez López, Julio|||0000-0002-3222-3036
author2_role author
author
author
dc.contributor.none.fl_str_mv Escuela Técnica Superior de Ingeniería de Telecomunicación
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
National Science Foundation, China
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Tensors
Generalized inverses
Moore Penrose inverse of tensors
Linear models
MATEMATICA APLICADA
topic Tensors
Generalized inverses
Moore Penrose inverse of tensors
Linear models
MATEMATICA APLICADA
description [EN] In this paper, we recall and extend some tensor operations. Then, the generalized inverse of tensors is established by using tensor equations. Moreover, we investigate the leastsquares solutions of tensor equations. An algorithm to compute the Moore Penrose inverse of an arbitrary tensor is constructed. Finally, we apply the obtained results to higher order Gauss Markov theorem
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/103606
url https://riunet.upv.es/handle/10251/103606
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11361009
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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