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A generalization of the inertia theorem for quadratic matrix polynomials

✍ Scribed by Bülent Bilir; Carmen Chicone

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
663 KB
Volume
280
Category
Article
ISSN
0024-3795

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✦ Synopsis

We show that the inertia of a quadratic matrix polynomial is determined in terms of the inertia of its coefficient matrices if the leading coefficient is Hermitian and nonsingular, the constant term is Hermitian, and the real part of the coefficient matrix of the first degree term is definite. In particular, we prove that the number of zero eigenvalues of such a matrix polynomial is the same as the number of zero eigenvalues of its constant term. We also give some new results for the case where the real part of the coefficient matrix of the first degree term is semidefinite.

📜 SIMILAR VOLUMES

A Generalization of Favard′s Theorem for
A Generalization of Favard′s Theorem for Polynomials Satisfying a Recurrence Relation
✍ A.J. Duran 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 744 KB

In this paper, we give the canonical expression for an inner product (defined in \(\mathscr{P}\), the linear space of real polynomials), for which the set of orthonormal polynomials satisfies a \((2 N+1)\)-term recurrence relation. This result is a generalization of Favard's theorem about orthogonal