Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Singular value estimates of oblique projections |
Autor: | Antezana, J.; Corach, G. |
Filiación: | Departamento de Matemática, FCE-UNLP, La Plata, Argentina Departamento de Matemática, FI-UBA, Buenos Aires, Argentina IAM-CONICET, Saavedra 15, (1083), Buenos Aires, Argentina
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Palabras clave: | Angle between subspaces; Generalized inverses; Projections; Banach spaces; Hilbert spaces; Angle between subspaces; Finite dimensional; Generalized inverses; Oblique projections; Projections; Singular values; Matrix algebra |
Año: | 2009
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Volumen: | 430
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Número: | 1
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Página de inicio: | 386
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Página de fin: | 395
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DOI: |
http://dx.doi.org/10.1016/j.laa.2008.08.001 |
Título revista: | Linear Algebra and Its Applications
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Título revista abreviado: | Linear Algebra Its Appl
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ISSN: | 00243795
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CODEN: | LAAPA
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00243795_v430_n1_p386_Antezana |
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Citas:
---------- APA ----------
Antezana, J. & Corach, G.
(2009)
. Singular value estimates of oblique projections. Linear Algebra and Its Applications, 430(1), 386-395.
http://dx.doi.org/10.1016/j.laa.2008.08.001---------- CHICAGO ----------
Antezana, J., Corach, G.
"Singular value estimates of oblique projections"
. Linear Algebra and Its Applications 430, no. 1
(2009) : 386-395.
http://dx.doi.org/10.1016/j.laa.2008.08.001---------- MLA ----------
Antezana, J., Corach, G.
"Singular value estimates of oblique projections"
. Linear Algebra and Its Applications, vol. 430, no. 1, 2009, pp. 386-395.
http://dx.doi.org/10.1016/j.laa.2008.08.001---------- VANCOUVER ----------
Antezana, J., Corach, G. Singular value estimates of oblique projections. Linear Algebra Its Appl. 2009;430(1):386-395.
http://dx.doi.org/10.1016/j.laa.2008.08.001