Approximation by Partial Isometries and Symmetric Approximation of Finite Frames

Autores
Antezana, Jorge Abel; Chiumiento, Eduardo Hernán
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
Facultad de Ciencias Exactas
Materia
Ciencias Exactas
Matemática
Partial isometry
Polar decomposition
Singular value decomposition
Symmetric approximation
Finite frame
Unitarily invariant norms
Löwdin orthogonalization
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/132306
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/132306
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network_name_str SEDICI (UNLP)
spelling Approximation by Partial Isometries and Symmetric Approximation of Finite FramesAntezana, Jorge AbelChiumiento, Eduardo HernánCiencias ExactasMatemáticaPartial isometryPolar decompositionSingular value decompositionSymmetric approximationFinite frameUnitarily invariant normsLöwdin orthogonalizationWe solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.Facultad de Ciencias Exactas2018-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1098-1118http://sedici.unlp.edu.ar/handle/10915/132306enginfo:eu-repo/semantics/altIdentifier/issn/1069-5869info:eu-repo/semantics/altIdentifier/issn/1531-5851info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-017-9547-5info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:31:18Zoai:sedici.unlp.edu.ar:10915/132306Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:31:18.674SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
spellingShingle Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
Antezana, Jorge Abel
Ciencias Exactas
Matemática
Partial isometry
Polar decomposition
Singular value decomposition
Symmetric approximation
Finite frame
Unitarily invariant norms
Löwdin orthogonalization
title_short Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_fullStr Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full_unstemmed Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_sort Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
dc.creator.none.fl_str_mv Antezana, Jorge Abel
Chiumiento, Eduardo Hernán
author Antezana, Jorge Abel
author_facet Antezana, Jorge Abel
Chiumiento, Eduardo Hernán
author_role author
author2 Chiumiento, Eduardo Hernán
author2_role author
dc.subject.none.fl_str_mv Ciencias Exactas
Matemática
Partial isometry
Polar decomposition
Singular value decomposition
Symmetric approximation
Finite frame
Unitarily invariant norms
Löwdin orthogonalization
topic Ciencias Exactas
Matemática
Partial isometry
Polar decomposition
Singular value decomposition
Symmetric approximation
Finite frame
Unitarily invariant norms
Löwdin orthogonalization
dc.description.none.fl_txt_mv We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
Facultad de Ciencias Exactas
description We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
publishDate 2018
dc.date.none.fl_str_mv 2018-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/132306
url http://sedici.unlp.edu.ar/handle/10915/132306
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1069-5869
info:eu-repo/semantics/altIdentifier/issn/1531-5851
info:eu-repo/semantics/altIdentifier/doi/10.1007/s00041-017-9547-5
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1098-1118
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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