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.