Perturbation theory for analytic matrix functions: The semisimple case

P. Lancaster, A. S. Markus, F. Zhou

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


The eigenvalue problem for non-self-adjoint, analytic matrix functions of two variables, L(λ,α), is examined with emphasis on the case when, at a fixed α0, L(λ. α0) has a multiple, semisimple eigenvalue λ0. New sufficient conditions for analytic dependence of eigenvalue functions, λ(α), on α in a neighborhood of α0 are obtained. An algorithm for generating Taylor coefficients of perturbed eigenvalues and eigenvectors is studied and the existence of positive radii of convergence is established. Connections with known results on self-adjoint problems are made.

Original languageEnglish
Pages (from-to)606-626
Number of pages21
JournalSIAM Journal on Matrix Analysis and Applications
Issue number3
StatePublished - 26 Jul 2004


  • Analytic matrix functions
  • Non-self-adjoint functions
  • Perturbation theory
  • Semisimple eigenvalues

ASJC Scopus subject areas

  • Analysis


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