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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 435730, 8 pages
http://dx.doi.org/10.1155/2013/435730
Research Article

Geometrical and Spectral Properties of the Orthogonal Projections of the Identity

Department of Mathematics, Research Institute SIANI, University of Las Palmas de Gran Canaria, Campus de Tafira, 35017 Las Palmas de Gran Canaria, Spain

Received 28 December 2012; Accepted 10 April 2013

Academic Editor: K. Sivakumar

Copyright © 2013 Luis González et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.