Lipschitz stability of canonical Jordan bases of H-selfadjoint matrices under structure-preserving perturbations

T. Bella, V. Olshevsky, U. Prasad

Research output: Contribution to journalArticlepeer-review

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Abstract

In this paper we study Jordan-structure-preserving perturbations of matrices selfadjoint in the indefinite inner product. The main result of the paper is Lipschitz stability of the corresponding affiliation matrices. The result can be reformulated as Lipschitz stability, under small perturbations, of canonical Jordan bases (i.e., eigenvectors and generalized eigenvectors enjoying a certain flipped orthonormality relation) of matrices selfadjoint in the indefinite inner product. The proof relies upon the analysis of small perturbations of invariant subspaces, where the size of a permutation of an invariant subspace is measured using the concepts of a gap and of a semigap.

Original languageEnglish
Pages (from-to)2130-2176
Number of pages47
JournalLinear Algebra and Its Applications
Volume428
Issue number8-9
DOIs
StatePublished - 15 Apr 2008

Keywords

  • Canonical Jordan bases
  • Gaps
  • Indefinite inner product
  • Invariant subspaces
  • Perturbations
  • Structure-preserving perturbations

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