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

Let {A,B}{A,B} be a definite matrix pair of order nn, and let the columns of X˜1∈Cn×l span an ll-dimensional approximate invariant eigenspace of {A,B}{A,B}. In this paper, we present a Hoffman–Wielandt-type residual bound for eigenvalues between Rayleigh quotient matrix pair {X˜1HAX˜1,X˜1HBX˜1} and {A,B}{A,B}, which extends a result of Kahan [W. Kahan, Numerical Linear Algebra, Canadian Mathematical Bulletin, 9 (1966) 757–801].