A Hoffman–Wielandt-type residual bound for generalized eigenvalues of a definite pair

Abstract: Let be a definite matrix pair of order , and let the columns of span an -dimensional approximate invariant eigenspace of . In this paper, we present a Hoffman–Wielandt-type residual bound for eigenvalues between Rayleigh quotient matrix pair and , which extends a result of Kahan [W. Kahan, Numerical Linear Algebra, Canadian Mathematical Bulletin, 9 (1966) 757–801]. [Copyright &y& Elsevier]