Journal of Mathematical Sciences

, Volume 176, Issue 1, pp 38–43 | Cite as

A characterization of the Toeplitz and Hankel circulants

  • Kh. D. Ikramov
  • V. N. Chugunov

A number of assertions of the following type are proved: A Toeplitz matrix T is a circulant if and only if T has an eigenvector e with unit components. These assertions characterize the circulants (and, more generally, the ϕ circulants), as well as their Hankel counterparts, in the sets of all Toeplitz and all Hankel matrices, respectively. Bibliography: 2 titles.


Russia Toeplitz Matrix Numerical Mathematic Unit Component Hankel Matrice 
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  1. 1.
    E. Bozzo, “Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices,” Linear Algebra Appl., 230, 12–15 (1995).MathSciNetCrossRefGoogle Scholar
  2. 2.
    Kh. D. Ikramov and N. V. Savel’eva, “On certain quasidiagonalizable matrix families,” Zh. Vyhisl. Matem. Matem. Fiz., 38, 1075–1084 (1998).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Moscow State UniversityMoscowRussia
  2. 2.Institute of Numerical MathematicsMoscowRussia

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