(untitled) (Journal of Computational Mathematics, 1991)
Let A,B be a definite matrix pair of order n, and let Z be an l-dimensional subspace of C^n. In this paper we introduce the Rayleigh quotient matrix pair H_1,K_1 and residual matrix pair R_A,R_B of A,B with respect to Z, and used the norm of R_A,R_B to bound the difference between the eigenvalues of H_1,K_1 and that of A,B, and to bound the difference between Z and an l-dimensional eigenspace of A,B. The corresponding classical theorems on the Hermitian matrices can be derived from the results of this paper.