A survey of the eigenstructure properties of finite Hermitian Toeplitz matrices

DOI10.1007/BF01195794zbMATH Open0658.47029MaRDI QIDQ1111149

Yves V. Genin

Publication date: 1987

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

algebraic structure of the Toeplitz eigenspaces of the zero location properties of their related eigenpolynomialsfunction theoretic interpretation of the eigenvalues and eigenvectors of a Hermitian Toeplitz matrixpseudo-Caratheodory and pseudo-lossless functions of finite index

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35)

Cites Work

• Parametric Toeplitz systems
• Toeplitz matrices commuting with tridiagonal matrices
• Eigenvalues and eigenvectors of symmetric centrosymmetric matrices
• Moment problems and low rank Toeplitz approximations
• Computing the Minimum Eigenvalue of a Symmetric Positive Definite Toeplitz Matrix
• Eigenvectors of a Toeplitz Matrix: Discrete Version of the Prolate Spheroidal Wave Functions
• Pseudo-lossless functions with application to the problem of locating the zeros of a polynomial
• On the eigenstructure of Toeplitz matrices
• A view of three decades of linear filtering theory
• Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty-V: The Discrete Case
• Über einige Fortsetzungsprobleme, die eng mit der Theorie hermitescher Operatoren im RaumeIIx zusammenhängen. I. Einige Funktionenklassen und ihre Darstellungen
• Hankel Forms, Toeplitz Forms and Meromorphic Functions
• Algebraic Structure of Generalized Positive Real Matrices
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM
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Related Items (5)

Inside the eigenvalues of certain Hermitian Toeplitz band matrices ⋮ The reconstruction of an Hermitian Toeplitz matrix with prescribed eigenpairs ⋮ Minimizing and maximizing the Euclidean norm of the product of two polynomials ⋮ On the zeros of eigenpolynomials of Hermitian Toeplitz matrices ⋮ Product rules for the displacement of near-Toeplitz matrices

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