Absolute and relative Weyl theorems for generalized eigenvalue problems

Weyl-type eigenvalue perturbation theories are derived for Hermitian definite pencils A - lambda B, in which B is positive definite. The results provide a one-to-one correspondence between the original and perturbed eigenvalues, and give a uniform perturbation bound. We give both absolute and relative perturbation results, defined in the standard Euclidean metric instead of the chordal metric that is often used. (C) 2009 Elsevier Inc. All rights reserved.