Zero distribution of matrix polynomials

DOI10.1016/j.laa.2007.04.001zbMath1132.15023OpenAlexW2093376619MaRDI QIDQ998205

Harry Dym, Dan Volok

Publication date: 27 August 2007

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2007.04.001

zbMATH Keywords

Riccati equationsdeterminantBézoutiansHermite theoremreproducing kernel Krein spacesSchur-Cohn theorem

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Matrix equations and identities (15A24) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Spaces with indefinite inner product (Kre?n spaces, Pontryagin spaces, etc.) (46C20) Matrices over function rings in one or more variables (15A54) Linear operators on spaces with an indefinite metric (47B50) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32)

Related Items (4)

Applications of de Branges Spaces of Vector-Valued Functions ⋮ On generalization of classical Hurwitz stability criteria for matrix polynomials ⋮ On the reproducing kernel of a Pontryagin space of vector valued polynomials ⋮ On the relation between Hurwitz stability of matrix polynomials and matrix-valued Stieltjes functions

Cites Work

• Algebraic methods for Toeplitz-like matrices and operators
• On hermitian block Hankel matrices, matrix polynomials, the Hamburger moment problem, interpolation and maximum entropy
• A new inertia theorem for Stein equations, inertia of invertible Hermitian block Toeplitz matrices and matrix orthogonal polynomials
• The Bezoutian and the eigenvalue-separation problem for matrix polynomials
• Bezout operators for analytic operator functions. I: A general concept of Bezout operator
• A Schur-Cohn theorem for matrix polynomials
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