Chinese J. Numer. Sinica., 11(1989) 24 ON PERTURBATION THEOREMS FOR THE GENERALIZED EIGENVALUES OF REGULAR MATRIX PAIRS† Ren-cang Li*

In this paper, we study the Bauer-Fike type theorems for regular matrix pairs and its general form. Besides these, we also obtain some bounds for measuring approximate generalized eigenvalues and for the perturbation of generalized eigenvalues concerning an approximate generalized invariant subspace. To estimate all these bounds, p-Hölder norm and an ad hoc pseudo-metric called p-Chordal matric which isn’t a metric on the Riemann sphere when p 6 = 2 are used. As to perturbations of eigenvalues of matrices, Bauer-Fike Theorem[3] is well-known, and its generalized version has also been deduced in Kahan et al.[5] and Li[6] so as to it can be applied to non-diagonalizable case. Note that the results in Li[6], which also generalize one of the results in Kahan et al.[5], improve slightly the results in [5]. On the other hand, for perturbations o