Singular value estimates of oblique projections
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,...
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Autores principales: | , |
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Formato: | Articulo |
Lenguaje: | Inglés |
Publicado: |
2009
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Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/82705 |
Aporte de: |
id |
I19-R120-10915-82705 |
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record_format |
dspace |
institution |
Universidad Nacional de La Plata |
institution_str |
I-19 |
repository_str |
R-120 |
collection |
SEDICI (UNLP) |
language |
Inglés |
topic |
Ciencias Exactas Angle between subspaces Generalized inverses Projections |
spellingShingle |
Ciencias Exactas Angle between subspaces Generalized inverses Projections Antezana, Jorge Abel Corach, Gustavo Singular value estimates of oblique projections |
topic_facet |
Ciencias Exactas Angle between subspaces Generalized inverses Projections |
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. |
format |
Articulo Articulo |
author |
Antezana, Jorge Abel Corach, Gustavo |
author_facet |
Antezana, Jorge Abel Corach, Gustavo |
author_sort |
Antezana, Jorge Abel |
title |
Singular value estimates of oblique 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 |
publishDate |
2009 |
url |
http://sedici.unlp.edu.ar/handle/10915/82705 |
work_keys_str_mv |
AT antezanajorgeabel singularvalueestimatesofobliqueprojections AT corachgustavo singularvalueestimatesofobliqueprojections |
bdutipo_str |
Repositorios |
_version_ |
1764820488545107974 |