aequationes mathematicae

, Volume 46, Issue 1–2, pp 44–55 | Cite as

Definitizable hermitian matrix pencils

  • Peter Lancaster
  • Qiang Ye
Research Papers


An hermitian matrix pencilλA − B withA nonsingular is called strongly definitizable ifAp(A−1B) is positive definite for some polynomialp. 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.

AMS (1980) subject classification

Primary 15A18m, 15A57 


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Copyright information

© Birkhäuser Verlag 1993

Authors and Affiliations

  • Peter Lancaster
    • 1
    • 2
  • Qiang Ye
    • 1
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Department of Mathematical SciencesUniversity of LethbridgeLethbridgeCanada

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