Spectral properties of finite Toeplitz matrices

  • P. Delsarte
  • Y. Genin
Conference paper

DOI: 10.1007/BFb0031053

Volume 58 of the book series Lecture Notes in Control and Information Sciences (LNCIS)
Cite this paper as:
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

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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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • P. Delsarte
    • 1
  • Y. Genin
    • 1
  1. 1.Philips Research Laboratory BrusselsBrusselsBelgium