On commuting matrices in Max algebra and in classical nonnegative algebra

Autores
Katz, Ricardo David; Schneider, Hans; Sergeev, Sergei
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector which directly leads to max analogs and nonnegative analogs of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we show how the intersection of eigencones of commuting matrices can be described and we consider connections with Boolean algebra which enables us to prove that two commuting irreducible matrices in max algebra have a common eigennode.
Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Schneider, Hans. University of Wisconsin; Estados Unidos
Fil: Sergeev, Sergei. The University Of Birmingham (tub);
Materia
COMMON EIGENVECTOR
COMMUTING MATRICES
FROBENIUS NORMAL FORM
MAX ALGEBRA
MAX-PLUS ALGEBRA
NONNEGATIVE MATRICES
PERRON-FROBENIUS
TROPICAL ALGEBRA
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/190093
Acceder
id CONICETDig_8fabb65d799564af871b9a2a080ad060
oai_identifier_str oai:ri.conicet.gov.ar:11336/190093
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On commuting matrices in Max algebra and in classical nonnegative algebraKatz, Ricardo DavidSchneider, HansSergeev, SergeiCOMMON EIGENVECTORCOMMUTING MATRICESFROBENIUS NORMAL FORMMAX ALGEBRAMAX-PLUS ALGEBRANONNEGATIVE MATRICESPERRON-FROBENIUSTROPICAL ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector which directly leads to max analogs and nonnegative analogs of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we show how the intersection of eigencones of commuting matrices can be described and we consider connections with Boolean algebra which enables us to prove that two commuting irreducible matrices in max algebra have a common eigennode.Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Schneider, Hans. University of Wisconsin; Estados UnidosFil: Sergeev, Sergei. The University Of Birmingham (tub);Elsevier Science Inc.2012-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/190093Katz, Ricardo David; Schneider, Hans; Sergeev, Sergei; On commuting matrices in Max algebra and in classical nonnegative algebra; Elsevier Science Inc.; Linear Algebra and its Applications; 436; 2; 9-2012; 276-2920024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379510004350info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2010.08.027info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:17:14Zoai:ri.conicet.gov.ar:11336/190093instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:17:14.842CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On commuting matrices in Max algebra and in classical nonnegative algebra
title On commuting matrices in Max algebra and in classical nonnegative algebra
spellingShingle On commuting matrices in Max algebra and in classical nonnegative algebra
Katz, Ricardo David
COMMON EIGENVECTOR
COMMUTING MATRICES
FROBENIUS NORMAL FORM
MAX ALGEBRA
MAX-PLUS ALGEBRA
NONNEGATIVE MATRICES
PERRON-FROBENIUS
TROPICAL ALGEBRA
title_short On commuting matrices in Max algebra and in classical nonnegative algebra
title_full On commuting matrices in Max algebra and in classical nonnegative algebra
title_fullStr On commuting matrices in Max algebra and in classical nonnegative algebra
title_full_unstemmed On commuting matrices in Max algebra and in classical nonnegative algebra
title_sort On commuting matrices in Max algebra and in classical nonnegative algebra
dc.creator.none.fl_str_mv Katz, Ricardo David
Schneider, Hans
Sergeev, Sergei
author Katz, Ricardo David
author_facet Katz, Ricardo David
Schneider, Hans
Sergeev, Sergei
author_role author
author2 Schneider, Hans
Sergeev, Sergei
author2_role author
author
dc.subject.none.fl_str_mv COMMON EIGENVECTOR
COMMUTING MATRICES
FROBENIUS NORMAL FORM
MAX ALGEBRA
MAX-PLUS ALGEBRA
NONNEGATIVE MATRICES
PERRON-FROBENIUS
TROPICAL ALGEBRA
topic COMMON EIGENVECTOR
COMMUTING MATRICES
FROBENIUS NORMAL FORM
MAX ALGEBRA
MAX-PLUS ALGEBRA
NONNEGATIVE MATRICES
PERRON-FROBENIUS
TROPICAL ALGEBRA
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector which directly leads to max analogs and nonnegative analogs of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we show how the intersection of eigencones of commuting matrices can be described and we consider connections with Boolean algebra which enables us to prove that two commuting irreducible matrices in max algebra have a common eigennode.
Fil: Katz, Ricardo David. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura. Instituto de Matemática "Beppo Levi"; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Schneider, Hans. University of Wisconsin; Estados Unidos
Fil: Sergeev, Sergei. The University Of Birmingham (tub);
description This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector which directly leads to max analogs and nonnegative analogs of some classical results for complex matrices. We also investigate Frobenius normal forms of commuting matrices, particularly when the Perron roots of the components are distinct. For the case of max algebra, we show how the intersection of eigencones of commuting matrices can be described and we consider connections with Boolean algebra which enables us to prove that two commuting irreducible matrices in max algebra have a common eigennode.
publishDate 2012
dc.date.none.fl_str_mv 2012-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/190093
Katz, Ricardo David; Schneider, Hans; Sergeev, Sergei; On commuting matrices in Max algebra and in classical nonnegative algebra; Elsevier Science Inc.; Linear Algebra and its Applications; 436; 2; 9-2012; 276-292
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/190093
identifier_str_mv Katz, Ricardo David; Schneider, Hans; Sergeev, Sergei; On commuting matrices in Max algebra and in classical nonnegative algebra; Elsevier Science Inc.; Linear Algebra and its Applications; 436; 2; 9-2012; 276-292
0024-3795
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379510004350
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2010.08.027
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc.
publisher.none.fl_str_mv Elsevier Science Inc.
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842980943515615232
score 12.993085

Publicaciones similares