Optimal Paths for Symmetric Actions in the Unitary Group

Autores
Antezana, Jorge Abel; Larotonda, Gabriel Andrés; Varela, Alejandro
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Given a positive and unitarily invariant Lagrangian L defined in the algebra of matrices, and a fixed time interval [0, t0 ] ⊂ ℝ, we study the action defined in the Lie group of n × n unitary matrices U(n) by, where α: [0, t0] → U(n) is a rectifiable curve. We prove that the one-parameter subgroups of U(n) are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in U(n) as well as angular metrics in the Grassmann manifold.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Larotonda, Gabriel Andrés. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
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
Geodesic Segment
Lagrangian
Optimal Path
Unitarily Invariant Norm
Unitary Group
Grassmann Manifold
Angular Metric
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:11336/37335
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Optimal Paths for Symmetric Actions in the Unitary GroupAntezana, Jorge AbelLarotonda, Gabriel AndrésVarela, AlejandroGeodesic SegmentLagrangianOptimal PathUnitarily Invariant NormUnitary GroupGrassmann ManifoldAngular Metrichttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a positive and unitarily invariant Lagrangian L defined in the algebra of matrices, and a fixed time interval [0, t0 ] ⊂ ℝ, we study the action defined in the Lie group of n × n unitary matrices U(n) by, where α: [0, t0] → U(n) is a rectifiable curve. We prove that the one-parameter subgroups of U(n) are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in U(n) as well as angular metrics in the Grassmann manifold.Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaFil: Larotonda, Gabriel Andrés. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: 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; ArgentinaSpringer2014-06info: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/11336/37335Antezana, Jorge Abel; Larotonda, Gabriel Andrés; Varela, Alejandro; Optimal Paths for Symmetric Actions in the Unitary Group; Springer; Communications In Mathematical Physics; 328; 2; 6-2014; 481-4970010-3616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00220-014-2041-xinfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-014-2041-xinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1107.2439info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:48Zoai:ri.conicet.gov.ar:11336/37335instacron: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 10:45:48.679CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal Paths for Symmetric Actions in the Unitary Group
title Optimal Paths for Symmetric Actions in the Unitary Group
spellingShingle Optimal Paths for Symmetric Actions in the Unitary Group
Antezana, Jorge Abel
Geodesic Segment
Lagrangian
Optimal Path
Unitarily Invariant Norm
Unitary Group
Grassmann Manifold
Angular Metric
title_short Optimal Paths for Symmetric Actions in the Unitary Group
title_full Optimal Paths for Symmetric Actions in the Unitary Group
title_fullStr Optimal Paths for Symmetric Actions in the Unitary Group
title_full_unstemmed Optimal Paths for Symmetric Actions in the Unitary Group
title_sort Optimal Paths for Symmetric Actions in the Unitary Group
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Larotonda, Gabriel Andrés
Varela, Alejandro
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Larotonda, Gabriel Andrés
Varela, Alejandro
author_role author
author2 Larotonda, Gabriel Andrés
Varela, Alejandro
author2_role author
author
dc.subject.none.fl_str_mv Geodesic Segment
Lagrangian
Optimal Path
Unitarily Invariant Norm
Unitary Group
Grassmann Manifold
Angular Metric
topic Geodesic Segment
Lagrangian
Optimal Path
Unitarily Invariant Norm
Unitary Group
Grassmann Manifold
Angular Metric
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Given a positive and unitarily invariant Lagrangian L defined in the algebra of matrices, and a fixed time interval [0, t0 ] ⊂ ℝ, we study the action defined in the Lie group of n × n unitary matrices U(n) by, where α: [0, t0] → U(n) is a rectifiable curve. We prove that the one-parameter subgroups of U(n) are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in U(n) as well as angular metrics in the Grassmann manifold.
Fil: Antezana, Jorge Abel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Fil: Larotonda, Gabriel Andrés. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
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 Given a positive and unitarily invariant Lagrangian L defined in the algebra of matrices, and a fixed time interval [0, t0 ] ⊂ ℝ, we study the action defined in the Lie group of n × n unitary matrices U(n) by, where α: [0, t0] → U(n) is a rectifiable curve. We prove that the one-parameter subgroups of U(n) are the optimal paths, provided the spectrum of the exponent is bounded by π. Moreover, if L is strictly convex, we prove that one-parameter subgroups are the unique optimal curves joining given endpoints. Finally, we also study the connection of these results with unitarily invariant metrics in U(n) as well as angular metrics in the Grassmann manifold.
publishDate 2014
dc.date.none.fl_str_mv 2014-06
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/11336/37335
Antezana, Jorge Abel; Larotonda, Gabriel Andrés; Varela, Alejandro; Optimal Paths for Symmetric Actions in the Unitary Group; Springer; Communications In Mathematical Physics; 328; 2; 6-2014; 481-497
0010-3616
CONICET Digital
CONICET
url http://hdl.handle.net/11336/37335
identifier_str_mv Antezana, Jorge Abel; Larotonda, Gabriel Andrés; Varela, Alejandro; Optimal Paths for Symmetric Actions in the Unitary Group; Springer; Communications In Mathematical Physics; 328; 2; 6-2014; 481-497
0010-3616
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/article/10.1007/s00220-014-2041-x
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00220-014-2041-x
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1107.2439
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 Springer
publisher.none.fl_str_mv Springer
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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