The generalized Levinger transformation

Abstract

In this paper, we present new results relating the numerical range of a matrix A with the generalized Levinger transformation L(A, alpha, beta) = alpha H(A) + beta S(A), where H(A) and S(A), are, respectively the Hermitian and skew-Hermitian parts of A. Using these results, we then derive expressions for eigenvalues and eigenvectors of the perturbed matrix A + L(E, alpha, beta), for a fixed matrix E and alpha, beta are real parameters. (C) 2009 Elsevier B.V. All rights reserved.