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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
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
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
Volumen:430
Número:1
Página de inicio:386
Página de fin:395
DOI: http://dx.doi.org/10.1016/j.laa.2008.08.001
Título revista:Linear Algebra and Its Applications
Título revista abreviado:Linear Algebra Its Appl
ISSN:00243795
CODEN:LAAPA
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