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On spectral variations under bounded real matrix perturbations

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In this paper we investigate the set of eigenvalues of a perturbed matrix {ie509-1} whereA is given and Δ∈∝n × n, |Δ|<ϱ is arbitrary. We determine a lower bound for thisspectral value set which is exact for normal matricesA with well separated eigenvalues. We also investigate the behaviour of the spectral value set under similarity transformations. The results are then applied tostability radii which measure the distance of a matrixA from the set of matrices having at least one eigenvalue in a given closed instability domain ℂb⊂ℂ.

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Authors and Affiliations

  1. Institut für Dynamische Systeme, Universität Bremen, W-2800, Bremen 33, Federal Republic of Germany

    D. Hinrichsen

  2. Control Theory Centre, University of Warwick, CV4 7AL, Coventry, UK

    A. J. Pritchard

Authors
  1. D. Hinrichsen
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  2. A. J. Pritchard
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Hinrichsen, D., Pritchard, A.J. On spectral variations under bounded real matrix perturbations. Numer. Math. 60, 509–524 (1991). https://doi.org/10.1007/BF01385734

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  • DOI: https://doi.org/10.1007/BF01385734

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