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Spectral properties of finite Toeplitz matrices

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Mathematical Theory of Networks and Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 58))

Abstract

The paper contains an investigation of certain spectral properties of finite Hermitian Toeplitz matrices. Some classical results relative to a constant Toeplitz matrix C are first extended to the polynomial matrix λI-C. Next, Carathéodory's representation based on the smallest eigenvalue of C is generalized to the case of an arbitrary eigenvalue. The splitting of each eigenspace of a real symmetric Toeplitz matrix C into its reciprocal and antireciprocal subspaces is then characterized. New identities are derived relating the characteristic determinants of the reciprocal and antireciprocal components of the Toeplitz submatrices of C. A special attention is brought to the inverse eigenvalue problem for Toeplitz matrices and some examples are given.

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Authors and Affiliations

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

    P. Delsarte & Y. Genin

Authors
  1. P. Delsarte
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  2. Y. Genin
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P. A. Fuhrmann

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© 1984 Springer-Verlag

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Delsarte, P., Genin, Y. (1984). Spectral properties of finite Toeplitz matrices. In: Fuhrmann, P.A. (eds) Mathematical Theory of Networks and Systems. Lecture Notes in Control and Information Sciences, vol 58. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0031053

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  • DOI: https://doi.org/10.1007/BFb0031053

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13168-7

  • Online ISBN: 978-3-540-38826-5

  • eBook Packages: Springer Book Archive

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