Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension

Autores
Andruchow, Esteban; Mata Lorenzo, Luis E.; Mendoza, Alberto; Recht, Lázaro; Varela, Alejandro
Año de publicación
2009
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In general C*-algebras, elements with minimal norm in some equivalence class are introduced and characterized. We study the set of minimal hermitian matrices, in the case where the C*-algebra consists of 3 × 3 complex matrices, and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matrices particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For the flag manifold of 'four mutually orthogonal complex lines' in C4, it is shown that there are infinitely many minimal curves joining arbitrarily close points. In the case of the flag manifold of 'three mutually orthogonal complex lines' in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does not occur.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Mata Lorenzo, Luis E.. Universidad Simón Bolivar; Venezuela
Fil: Mendoza, Alberto. Universidad Simón Bolivar; Venezuela
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simón Bolivar; Venezuela
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Materia
APPROXIMATION
CURVES
FLAG MANIFOLDS
MATRICES
MINIMAL
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:11336/97240
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Minimal matrices and the corresponding minimal curves on flag manifolds in low dimensionAndruchow, EstebanMata Lorenzo, Luis E.Mendoza, AlbertoRecht, LázaroVarela, AlejandroAPPROXIMATIONCURVESFLAG MANIFOLDSMATRICESMINIMALhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In general C*-algebras, elements with minimal norm in some equivalence class are introduced and characterized. We study the set of minimal hermitian matrices, in the case where the C*-algebra consists of 3 × 3 complex matrices, and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matrices particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For the flag manifold of 'four mutually orthogonal complex lines' in C4, it is shown that there are infinitely many minimal curves joining arbitrarily close points. In the case of the flag manifold of 'three mutually orthogonal complex lines' in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does not occur.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Mata Lorenzo, Luis E.. Universidad Simón Bolivar; VenezuelaFil: Mendoza, Alberto. Universidad Simón Bolivar; VenezuelaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simón Bolivar; VenezuelaFil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaElsevier Science Inc2009-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/97240Andruchow, Esteban; Mata Lorenzo, Luis E.; Mendoza, Alberto; Recht, Lázaro; Varela, Alejandro; Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension; Elsevier Science Inc; Linear Algebra and its Applications; 430; 8-9; 4-2009; 1906-19280024-3795CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2008.10.023info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379508005107info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:37:10Zoai:ri.conicet.gov.ar:11336/97240instacron: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:34982025-09-29 09:37:10.761CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
title Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
spellingShingle Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
Andruchow, Esteban
APPROXIMATION
CURVES
FLAG MANIFOLDS
MATRICES
MINIMAL
title_short Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
title_full Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
title_fullStr Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
title_full_unstemmed Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
title_sort Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension
dc.creator.none.fl_str_mv Andruchow, Esteban
Mata Lorenzo, Luis E.
Mendoza, Alberto
Recht, Lázaro
Varela, Alejandro
author Andruchow, Esteban
author_facet Andruchow, Esteban
Mata Lorenzo, Luis E.
Mendoza, Alberto
Recht, Lázaro
Varela, Alejandro
author_role author
author2 Mata Lorenzo, Luis E.
Mendoza, Alberto
Recht, Lázaro
Varela, Alejandro
author2_role author
author
author
author
dc.subject.none.fl_str_mv APPROXIMATION
CURVES
FLAG MANIFOLDS
MATRICES
MINIMAL
topic APPROXIMATION
CURVES
FLAG MANIFOLDS
MATRICES
MINIMAL
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In general C*-algebras, elements with minimal norm in some equivalence class are introduced and characterized. We study the set of minimal hermitian matrices, in the case where the C*-algebra consists of 3 × 3 complex matrices, and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matrices particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For the flag manifold of 'four mutually orthogonal complex lines' in C4, it is shown that there are infinitely many minimal curves joining arbitrarily close points. In the case of the flag manifold of 'three mutually orthogonal complex lines' in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does not occur.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Mata Lorenzo, Luis E.. Universidad Simón Bolivar; Venezuela
Fil: Mendoza, Alberto. Universidad Simón Bolivar; Venezuela
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simón Bolivar; Venezuela
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
description In general C*-algebras, elements with minimal norm in some equivalence class are introduced and characterized. We study the set of minimal hermitian matrices, in the case where the C*-algebra consists of 3 × 3 complex matrices, and the quotient is taken by the subalgebra of diagonal matrices. We thoroughly study the set of minimal matrices particularly because of its relation to the geometric problem of finding minimal curves in flag manifolds. For the flag manifold of 'four mutually orthogonal complex lines' in C4, it is shown that there are infinitely many minimal curves joining arbitrarily close points. In the case of the flag manifold of 'three mutually orthogonal complex lines' in C3, we show that the phenomenon of multiple minimal curves joining arbitrarily close points does not occur.
publishDate 2009
dc.date.none.fl_str_mv 2009-04
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/11336/97240
Andruchow, Esteban; Mata Lorenzo, Luis E.; Mendoza, Alberto; Recht, Lázaro; Varela, Alejandro; Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension; Elsevier Science Inc; Linear Algebra and its Applications; 430; 8-9; 4-2009; 1906-1928
0024-3795
CONICET Digital
CONICET
url http://hdl.handle.net/11336/97240
identifier_str_mv Andruchow, Esteban; Mata Lorenzo, Luis E.; Mendoza, Alberto; Recht, Lázaro; Varela, Alejandro; Minimal matrices and the corresponding minimal curves on flag manifolds in low dimension; Elsevier Science Inc; Linear Algebra and its Applications; 430; 8-9; 4-2009; 1906-1928
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/doi/10.1016/j.laa.2008.10.023
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0024379508005107
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
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
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score 13.070432

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