Nongeneric eigenvalue perturbations of Jordan blocks

Yanyuan Ma, Alan Edelman

Research output: Contribution to journalArticle

23 Scopus citations

Abstract

We show that if an n X n Jordan block is perturbed by an O(ε) upper k-Hessenberg matrix (k subdiagonals including the main diagonal), then generically the eigenvalues split into p rings of size k and one of size r (if r ≠ 0), where n = pk + r. This generalizes the familiar result (k = n, p = 1, r = 0) that generically the eigenvalues split into a ring of size n. We compute the radii of the rings to first order and generalize the result in a number of directions involving multiple Jordan blocks of the same size.

Original languageEnglish (US)
Pages (from-to)45-63
Number of pages19
JournalLinear Algebra and Its Applications
Volume273
Issue number1-3
DOIs
StatePublished - Apr 1 1998

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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