## $\mu$-values and spectral value sets for linear perturbation classes defined by a scalar product

Please always quote using this URN: urn:nbn:de:0296-matheon-4188

We study the variation of the spectrum of matrices under perturbations which are self- or skew-adjoint with respect to a scalar product. Computable formulae are given for the associated $\mu$-values. The results can be used to calculate spectral value sets for the perturbation classes under consideration. We discuss the special case of complex Hamiltonian perturbations of a Hamiltonian matrix in detail.

Author: Michael Karow urn:nbn:de:0296-matheon-4188 Volker Mehrmann English 27.09.2007 15A57 $\mu$-values; eigenvalues; linear systems; perturbations; spectral value sets 15A18 Eigenvalues, singular values, and eigenvectors 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx] 93C05 Linear systems 93C73 Perturbations Matheon Preprint #406