The generalized Levinger transformation

摘要

In this paper, we present new results relating the numerical range of a matrix A with the generalized Levinger transformation L(A,α,β)=αHA+βSA, where HA and SA, 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.