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A characterization of the Toeplitz and Hankel circulants

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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.

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References

  1. E. Bozzo, “Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices,” Linear Algebra Appl., 230, 12–15 (1995).

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  2. Kh. D. Ikramov and N. V. Savel’eva, “On certain quasidiagonalizable matrix families,” Zh. Vyhisl. Matem. Matem. Fiz., 38, 1075–1084 (1998).

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Correspondence to Kh. D. Ikramov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 382, 2010, pp. 71–81.

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Ikramov, K.D., Chugunov, V.N. A characterization of the Toeplitz and Hankel circulants. J Math Sci 176, 38–43 (2011). https://doi.org/10.1007/s10958-011-0391-x

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  • DOI: https://doi.org/10.1007/s10958-011-0391-x

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