Definitizable hermitian matrix pencils

Peter Lancaster; Qiang Ye

doi:10.1007/BF01833997

Definitizable hermitian matrix pencils

Peter Lancaster, Qiang Ye

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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 language	English
Pages (from-to)	44-55
Number of pages	12
Journal	Aequationes Mathematicae
Volume	46
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01833997
State	Published - Aug 1993

Keywords

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

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/BF01833997

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abstract = "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.",

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AU - Ye, Qiang

PY - 1993/8

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N2 - 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.

AB - 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.

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

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DO - 10.1007/BF01833997

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JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

IS - 1-2

ER -

Definitizable hermitian matrix pencils

Abstract

Keywords

ASJC Scopus subject areas

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