$\mu$-values and spectral value sets for linear perturbation classes defined by a scalar product
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.
|Date of first Publication:||27.09.2007|
|Tag:||$\mu$-values; eigenvalues; linear systems; perturbations; spectral value sets|
|MSC-Classification:||15A18 Eigenvalues, singular values, and eigenvectors|
|15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx]|
|93C05 Linear systems|
|Preprint Number:||Matheon Preprint #406|