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 let $(\mu,u)$ be a Ritz pair from a subspace $\clk$ of
$\comp^{2}$. Saad has given a simple inequality bounding
$\sin\angle(x,u)$ in terms of $\sin\angle(x,\clk)$. In this note we
show that this inequality can be extended to an equally simple
inequality for eigenspaces of non-Hermitian matrices.
(Also cross-referenced as UMIACS-TR-99-78)