Normalized Frobenius condition number of the orthogonal projections of the identity

This paper deals with the orthogonal projection (in the Frobenius sense) AN of the identity matrix I onto the matrix subspace AS (A is an element of R-nxn, S being an arbitrary subspace of R-nxn). Lower and upper bounds on the normalized Frobenius condition number of matrix AN are given. Furthermore, for every matrix subspace S subset of R-nxn, a new index (kappa) over cap (F) (A, S), which generalizes the normalized Frobenius condition number of matrix A, is defined and analyzed. (C) 2012 Elsevier Inc. All rights reserved.