Definitizable hermitian matrix pencils

Peter Lancaster, Qiang Ye

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


An hermitian matrix pencil λA - B with A nonsingular is called strongly definitizable if Ap(A-1B) is positive definite for some polynomial p. We present three characterizations of strongly definitizable pencils, which generalize the classical results for definite pencils. They are, in particular, stably simultaneously diagonable. We also discuss this form of stability with respect to an open subset of the real line. Implications for some quadratic eigenvalue problems are included.

Original languageEnglish
Pages (from-to)44-55
Number of pages12
JournalAequationes Mathematicae
Issue number1-2
StatePublished - Aug 1993


  • AMS (1980) subject classification: Primary 15A18m, 15A57

ASJC Scopus subject areas

  • General Mathematics
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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