A MATRIX PAIR OF AN ALMOST DIAGONAL SKEW-SYMMETRICAL MATRIX AND A SYMMETRICAL POSITIVE-DEFINITE MATRIX

Let A be skew-symmetric, B be symmetric positive definite, and the pai r (A, B) have multiple eigenvalues. If A is close to Murnaghan form an d B is close to diagonal form, then certain principal submatrices of A and B are specially related. In this paper we describe this relations hip and quantify it under the usual asymptotic conditions. If B = I, t he identity matrix, the result describes a special structure of a skew -symmetric matrix almost in Murnaghan form. We then briefly discuss ho w the Paardekooper method for skew-symmetric matrices asymptotically b ehaves in the presence of multiple eigenvalues.