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⊥, and let PW {norm of matrix} M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW {norm of matrix} M⊥2 (sk (PW {norm of matr...
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2009
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v430_n1_p386_Antezana http://hdl.handle.net/20.500.12110/paper_00243795_v430_n1_p386_Antezana |
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paper:paper_00243795_v430_n1_p386_Antezana2023-06-08T14:52:06Z Singular value estimates of oblique projections Angle between subspaces Generalized inverses Projections Banach spaces Hilbert spaces Angle between subspaces Finite dimensional Generalized inverses Oblique projections Projections Singular values Matrix algebra Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M⊥, and let PW {norm of matrix} M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW {norm of matrix} M⊥2 (sk (PW {norm of matrix} M⊥) - 1) = under(min, (F, H) ∈ X (W, M))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* = PW {norm of matrix} M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained. © 2008 Elsevier Inc. All rights reserved. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v430_n1_p386_Antezana http://hdl.handle.net/20.500.12110/paper_00243795_v430_n1_p386_Antezana |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Angle between subspaces Generalized inverses Projections Banach spaces Hilbert spaces Angle between subspaces Finite dimensional Generalized inverses Oblique projections Projections Singular values Matrix algebra |
| spellingShingle |
Angle between subspaces Generalized inverses Projections Banach spaces Hilbert spaces Angle between subspaces Finite dimensional Generalized inverses Oblique projections Projections Singular values Matrix algebra Singular value estimates of oblique projections |
| topic_facet |
Angle between subspaces Generalized inverses Projections Banach spaces Hilbert spaces Angle between subspaces Finite dimensional Generalized inverses Oblique projections Projections Singular values Matrix algebra |
| description |
Let W and M be two finite dimensional subspaces of a Hilbert space H such that H = W ⊕ M⊥, and let PW {norm of matrix} M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW {norm of matrix} M⊥2 (sk (PW {norm of matrix} M⊥) - 1) = under(min, (F, H) ∈ X (W, M))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* = PW {norm of matrix} M⊥, and k ∈ {1, ..., dim W}. We also characterize all the pairs where the minimum is attained. © 2008 Elsevier Inc. All rights reserved. |
| 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 |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v430_n1_p386_Antezana http://hdl.handle.net/20.500.12110/paper_00243795_v430_n1_p386_Antezana |
| _version_ |
1768542633675718656 |