Optimal Paths for Symmetric Actions in the Unitary Group

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Antezana, Jorge Abel, Larotonda, Gabriel, Varela, Alejandro
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2014
Materias:
Matemática
Geodesic segment
Lagrangian
Optimal path
Unitarily invariant norm
Unitary group
Grassmann manifold
Angular metric
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/99737
https://ri.conicet.gov.ar/11336/37335
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-99737
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Geodesic segment
Lagrangian
Optimal path
Unitarily invariant norm
Unitary group
Grassmann manifold
Angular metric
spellingShingle Matemática
Geodesic segment
Lagrangian
Optimal path
Unitarily invariant norm
Unitary group
Grassmann manifold
Angular metric
Antezana, Jorge Abel
Larotonda, Gabriel
Varela, Alejandro
Optimal Paths for Symmetric Actions in the Unitary Group
topic_facet Matemática
Geodesic segment
Lagrangian
Optimal path
Unitarily invariant norm
Unitary group
Grassmann manifold
Angular metric
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.
format Articulo
Preprint
author Antezana, Jorge Abel
Larotonda, Gabriel
Varela, Alejandro
author_facet Antezana, Jorge Abel
Larotonda, Gabriel
Varela, Alejandro
author_sort Antezana, Jorge Abel
title Optimal Paths for Symmetric Actions in the Unitary Group
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
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/99737
https://ri.conicet.gov.ar/11336/37335
work_keys_str_mv AT antezanajorgeabel optimalpathsforsymmetricactionsintheunitarygroup
AT larotondagabriel optimalpathsforsymmetricactionsintheunitarygroup
AT varelaalejandro optimalpathsforsymmetricactionsintheunitarygroup
bdutipo_str Repositorios
_version_ 1764820493234339843

Ejemplares similares