A generalization of Saad's theorem on Rayleigh-Ritz approximations

Let (lambda ,x) be an eigenpair of the Hermitian matrix A of order n and le t (mu, u) be a Ritz pail from a subspace K of C-2. Y. Saad (Numerical Metho ds for Large Eigenvalue Problems: Theory and Algorithm, Wiley, New York, 19 92) has given a simple inequality bounding sin angle (x, u) in terms of sin L(x, K). In this paper, we show that this inequality can be extended to an equally simple inequality for eigenspaces of non-Hermitian matrices, (C) 2 001 Elsevier Science Inc. All rights reserved.