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