Geodesic
A characterization of Toeplitz and Hankel circulants
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 71-81 Cet article a éte moissonné depuis la source Math-Net.Ru

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A number of propositions of the following type is proved: A Toeplitz matrix $T$ is a circulant if and only if $T$ has an eigenvector $e$ with all the components equal to one. These propositions characterize the circulants (and, more generally, the $\phi$-circulants), as well as their Hankel counterparts, in the sets of all Toeplitz and Hankel matrices, respectively. Bibl. 2 titles. 
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Kh. D. Ikramov; V. N. Chugunov. A characterization of Toeplitz and Hankel circulants. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIII, Tome 382 (2010), pp. 71-81. http://geodesic.mathdoc.fr/item/ZNSL_2010_382_a6/

[1] E. Bozzo, “Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices”, Linear Algebra Appl., 230 (1995), 120–150 | DOI | MR

[2] Kh. D. Ikramov, N. V. Saveleva, “O nekotorykh kvazidiagonalizuemykh semeistvakh matrits”, Zh. vychisl. matem. i matem. fiz., 38:7 (1998), 1075–1084 | MR | Zbl