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