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Perturbations of Jordan matrices

Authors
Publisher
Academic Press Inc Elsevier Science
Publication Date
Keywords
  • Pseudospectrum
  • Spectrum
  • Random Matrices
  • Lidskii
  • Perturbations
  • Jordan Matrices
  • Eigenvalues
  • Mathematics And Statistics

Abstract

We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In the case of random perturbations we obtain explicit estimates which show that as the size of the matrix increases, most of the eigenvalues of the perturbed matrix converge to a certain circle with centre at the origin. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases. (C) 2008 Elsevier Inc. All fights reserved.

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