Transformation.

In this paper, we present new results relating the numerical range of a matrix A with generalized Levinger transformation L(A, α, β) = αH A + βS 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, α, β), for a fixed matrix E and α, β are real parameters.