Definitizable hermitian matrix pencils
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An hermitian matrix pencilλA − B withA nonsingular is called strongly definitizable ifAp(A−1B) 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.
AMS (1980) subject classificationPrimary 15A18m, 15A57
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