Singular value estimates of oblique projections

Autores: Antezana, Jorge Abel; Corach, Gustavo
Año de publicación: 2009
Idioma: inglés
Tipo de recurso: artículo
Estado: versión publicada
Descripción: Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M>SUP>⊥, and let PW ‖ M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of P W‖M⊥: 2 (sk (P W ‖ M⊥) - 1) = min, (F, H) ∈ X (W, M) Sk (F - H)²,where the minimum is taken over the set of all operator pairs (F, H) on H such that R (F) = W, R (H) = M and FH* = P W ‖ M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained.
Facultad de Ciencias Exactas
Materia: Ciencias Exactas
Angle between subspaces
Generalized inverses
Projections
Nivel de accesibilidad: acceso abierto
Condiciones de uso: http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
Institución: Universidad Nacional de La Plata
OAI Identificador: oai:sedici.unlp.edu.ar:10915/82705

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spelling	Singular value estimates of oblique projectionsAntezana, Jorge AbelCorach, GustavoCiencias ExactasAngle between subspacesGeneralized inversesProjectionsLet W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M>SUP>⊥</SUP>, and let PW ‖ M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of P W‖M⊥: 2 (sk (P W ‖ M⊥) - 1) = min, (F, H) ∈ X (W, M) Sk (F - H)<SUP>2</SUP>,where the minimum is taken over the set of all operator pairs (F, H) on H such that R (F) = W, R (H) = M and FH* = P W ‖ M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained.Facultad de Ciencias Exactas2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf386-395http://sedici.unlp.edu.ar/handle/10915/82705enginfo:eu-repo/semantics/altIdentifier/issn/0024-3795info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2008.08.001info: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:UNLP2025-10-15T11:07:32Zoai:sedici.unlp.edu.ar:10915/82705Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:07:32.742SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv	Singular value estimates of oblique projections
title	Singular value estimates of oblique projections
spellingShingle	Singular value estimates of oblique projections Antezana, Jorge Abel Ciencias Exactas Angle between subspaces Generalized inverses Projections
title_short	Singular value estimates of oblique projections
title_full	Singular value estimates of oblique projections
title_fullStr	Singular value estimates of oblique projections
title_full_unstemmed	Singular value estimates of oblique projections
title_sort	Singular value estimates of oblique projections
dc.creator.none.fl_str_mv	Antezana, Jorge Abel Corach, Gustavo
author	Antezana, Jorge Abel
author_facet	Antezana, Jorge Abel Corach, Gustavo
author_role	author
author2	Corach, Gustavo
author2_role	author
dc.subject.none.fl_str_mv	Ciencias Exactas Angle between subspaces Generalized inverses Projections
topic	Ciencias Exactas Angle between subspaces Generalized inverses Projections
dc.description.none.fl_txt_mv	Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M>SUP>⊥</SUP>, and let PW ‖ M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of P W‖M⊥: 2 (sk (P W ‖ M⊥) - 1) = min, (F, H) ∈ X (W, M) Sk (F - H)<SUP>2</SUP>,where the minimum is taken over the set of all operator pairs (F, H) on H such that R (F) = W, R (H) = M and FH* = P W ‖ M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained. Facultad de Ciencias Exactas
description	Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M>SUP>⊥</SUP>, and let PW ‖ M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of P W‖M⊥: 2 (sk (P W ‖ M⊥) - 1) = min, (F, H) ∈ X (W, M) Sk (F - H)<SUP>2</SUP>,where the minimum is taken over the set of all operator pairs (F, H) on H such that R (F) = W, R (H) = M and FH* = P W ‖ M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained.
publishDate	2009
dc.date.none.fl_str_mv	2009
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/10915/82705
url	http://sedici.unlp.edu.ar/handle/10915/82705
dc.language.none.fl_str_mv	eng
language	eng
dc.relation.none.fl_str_mv	info:eu-repo/semantics/altIdentifier/issn/0024-3795 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2008.08.001
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 386-395
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
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Singular value estimates of oblique projections

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