# A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations

 Title A Generalization of Saad's Theorem on Rayleigh-Ritz Approximations Publication Type Reports Year of Publication 2000 Authors Stewart G.W Date Published 2000/02/04/ Institution Instititue for Advanced Computer Studies, Univ of Maryland, College Park Keywords Technical Report Abstract 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) URL http://drum.lib.umd.edu/handle/1903/1050