Generalized eigenvalues of a definite Hermitian matrix pair

In this note, we study some basic properties of generalized eigenvalues of a definite Hermitian matrix pair. In particular, we prove an interlacing theorem and a minimax theorem. We also obtain upper bounds for the variation of the generalized eigenvalues under perturbation. These results extend and improve those of R.-C. Li, J.-g. Sun, and G.W. Stewart on the topic. (C) 1998 Elsevier Science Inc.