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μ-values and spectral value sets for linear perturbation classes defined by a scalar product

Karow, Michael

We study the variation of the spectrum of matrices under perturbations which are self- or skew-adjoint with respect to a scalar product. Computable formulas are given for the associated μ-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.
Published in: SIAM Journal on Matrix Analysis and Applications, 10.1137/090774896, Society for Industrial and Applied Mathematics