Global Properties of Eigenvalues of Parametric Rank One Perturbations for Unstructured and Structured Matrices

摘要

General properties of eigenvalues of A + tau uv* as functions of tau is an element of C or tau is an element of R or T = tau = e(i theta) on the unit circle are considered. In particular, the problem of existence of global analytic formulas for eigenvalues is addressed. Furthermore, the limits of eigenvalues with tau -> infinity are discussed in detail. The following classes of matrices are considered: complex (without additional structure), real (without additional structure), complex H-selfadjoint and real J-Hamiltonian.