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$\mu$-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.

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Metadaten
Author:Michael Karow
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
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