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A survey of the eigenstructure properties of finite Hermitian Toeplitz matrices

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Abstract

This paper is concerned with a survey of the spectral properties of finite Hermitian Toeplitz matrices. It contains in particular a detailed analysis of the algebraic structure of the Toeplitz eignespaces and of the zero location properties of their related eignepolynomials. The theory of pseudo-Carathéodory and pseudo-lossless functions of finite index is shown to provide a function theoretic interpretation of the eigenvalues and eigenvectors of a Hermitian Teoplitz matrix; most known results in the field fit naturally into this fremework.

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  1. Philips Research Laboratory Brussels, 2, avenue Van Becelaere, Box 8, B-1170, Brussels, Belgium

    Yves Genin

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  1. Yves Genin
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Genin, Y. A survey of the eigenstructure properties of finite Hermitian Toeplitz matrices. Integr equ oper theory 10, 621–639 (1987). https://doi.org/10.1007/BF01195794

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