Definitizable hermitian matrix pencils

Summary An hermitian matrix pencilA – B withA nonsingular is called strongly definitizable ifAp(A ^–1 B) is positive definite for some polynomialp. We present three characterizations of strongly definitizable pencils, which generalize the classical results for definite pencils. They are, in particular, stably simultaneously diagonable. We also discuss this form of stability with respect to an open subset of the real line. Implications for some quadratic eigenvalue problems are included.Research supported in part by the National Sciences and Engineering Research Council of Canada.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth.