Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

We analyze the best approximation (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace ( nonsingular, being any fixed subspace of ). Some new geometrical and spectral properties of the orthogonal projection are derived. In particular, new inequalities for the trace and...

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Main Authors: Luis González, Antonio Suárez, Dolores García
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/435730
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spelling doaj-28d78aad73e844579195eabb333a65c02020-11-24T21:23:19ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/435730435730Geometrical and Spectral Properties of the Orthogonal Projections of the IdentityLuis González0Antonio Suárez1Dolores García2Department of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, SpainDepartment of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, SpainDepartment of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, SpainWe analyze the best approximation (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace ( nonsingular, being any fixed subspace of ). Some new geometrical and spectral properties of the orthogonal projection are derived. In particular, new inequalities for the trace and for the eigenvalues of matrix are presented for the special case that is symmetric and positive definite.http://dx.doi.org/10.1155/2013/435730
collection DOAJ
language English
format Article
sources DOAJ
author Luis González
Antonio Suárez
Dolores García
spellingShingle Luis González
Antonio Suárez
Dolores García
Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
Journal of Applied Mathematics
author_facet Luis González
Antonio Suárez
Dolores García
author_sort Luis González
title Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
title_short Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
title_full Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
title_fullStr Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
title_full_unstemmed Geometrical and Spectral Properties of the Orthogonal Projections of the Identity
title_sort geometrical and spectral properties of the orthogonal projections of the identity
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description We analyze the best approximation (in the Frobenius sense) to the identity matrix in an arbitrary matrix subspace ( nonsingular, being any fixed subspace of ). Some new geometrical and spectral properties of the orthogonal projection are derived. In particular, new inequalities for the trace and for the eigenvalues of matrix are presented for the special case that is symmetric and positive definite.
url http://dx.doi.org/10.1155/2013/435730
work_keys_str_mv AT luisgonzalez geometricalandspectralpropertiesoftheorthogonalprojectionsoftheidentity
AT antoniosuarez geometricalandspectralpropertiesoftheorthogonalprojectionsoftheidentity
AT doloresgarcia geometricalandspectralpropertiesoftheorthogonalprojectionsoftheidentity
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