Two Simple Residual Bounds for the Eigenvalues of Hermitian Matrices

Let $A$ be Hermitian and let the orthonormal columns of $X$ span anapproximate invariant subspace of $X$. Then the residual $R = AX-XM$
$(M=X\ctp AX)$ will be small. The theorems of this paper bound the
distance of the spectrum of $M$ from the spectrum of $A$ in terms of
appropriate norms of $R$.
Appeared in SIAM J. Mat. Anal. Appl. 12 (1991) 205--208.
(Also cross-referenced as UMIACS-TR-89-123)