Approximation by Partial Isometries and Symmetric Approximation of Finite Frames

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a s...

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Detalles Bibliográficos
Autores principales:	Antezana, Jorge Abel, Chiumiento, Eduardo Hernán
Formato:	Articulo
Lenguaje:	Inglés
Publicado:	2018
Materias:	Ciencias Exactas Matemática Partial isometry Polar decomposition Singular value decomposition Symmetric approximation Finite frame Unitarily invariant norms Löwdin orthogonalization
Acceso en línea:	http://sedici.unlp.edu.ar/handle/10915/132306
Aporte de:	SEDICI (UNLP) de Universidad Nacional de La Plata

id	I19-R120-10915-132306
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 Matemática Partial isometry Polar decomposition Singular value decomposition Symmetric approximation Finite frame Unitarily invariant norms Löwdin orthogonalization
spellingShingle	Ciencias Exactas Matemática Partial isometry Polar decomposition Singular value decomposition Symmetric approximation Finite frame Unitarily invariant norms Löwdin orthogonalization Antezana, Jorge Abel Chiumiento, Eduardo Hernán Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
topic_facet	Ciencias Exactas Matemática Partial isometry Polar decomposition Singular value decomposition Symmetric approximation Finite frame Unitarily invariant norms Löwdin orthogonalization
description	We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize all the solutions. In particular, this allows us to give a simple necessary and sufficient condition for uniqueness. We then apply these results to solve the global problem of approximation by partial isometries, and to extend the notion of symmetric approximation of frames introduced in Frank et al. (Trans Am Math Soc 354: 777–793, 2002). In addition, we characterize symmetric approximations of frames belonging to a prescribed subspace.
format	Articulo Articulo
author	Antezana, Jorge Abel Chiumiento, Eduardo Hernán
author_facet	Antezana, Jorge Abel Chiumiento, Eduardo Hernán
author_sort	Antezana, Jorge Abel
title	Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_short	Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full	Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_fullStr	Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_full_unstemmed	Approximation by Partial Isometries and Symmetric Approximation of Finite Frames
title_sort	approximation by partial isometries and symmetric approximation of finite frames
publishDate	2018
url	http://sedici.unlp.edu.ar/handle/10915/132306
work_keys_str_mv	AT antezanajorgeabel approximationbypartialisometriesandsymmetricapproximationoffiniteframes AT chiumientoeduardohernan approximationbypartialisometriesandsymmetricapproximationoffiniteframes
bdutipo_str	Repositorios
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Approximation by Partial Isometries and Symmetric Approximation of Finite Frames

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