$\mu$-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 |
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URN: | urn:nbn:de:0296-matheon-4188 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2007/09/27 |
Release Date: | 2007/09/27 |
Tag: | |
MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A18 Eigenvalues, singular values, and eigenvectors |
15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A63 Quadratic and bilinear forms, inner products [See mainly 11Exx] | |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C05 Linear systems | |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C73 Perturbations | |
Preprint Number: | 406 |