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 pa
✦ LIBER ✦
A Generalization of the One-Step Theorem for Matrix Polynomials
✍ Scribed by R. L. Ellis; I. Gohberg
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2003
- Tongue
- English
- Weight
- 222 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0378-620X
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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