Geodesic
On eigenvalues of $(T+H)$-circulants and $(T+H)$-skew-circulants
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 2, pp. 111-124 
A. K. Abdikalykov; Kh. D. Ikramov; V. N. Chugunov. On eigenvalues of $(T+H)$-circulants and $(T+H)$-skew-circulants. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 2, pp. 111-124. http://geodesic.mathdoc.fr/item/SJVM_2014_17_2_a2/
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     title = {On eigenvalues of $(T+H)$-circulants and $(T+H)$-skew-circulants},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Explicit formulas for calculating eigenvalues of the Hankel circulants, Hankel skew-circulants, $(T+H)$-circulants, and $(T+H)$-skew-circulants are obtained. It is shown that if $\phi\ne\pm1$, then the set of matrices that can be represented as sums of a Toeplitz $\phi$-circulant and a Hankel $\phi$-circulant is not an algebra.

[1] Bozzo E., “Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices”, Linear Algebra Appl., 230 (1995), 127–150 | DOI | MR | Zbl

[2] Voevodin V. V., Tyrtyshnikov E. E., Vychislitelnye protsessy s teplitsevymi matritsami, Nauka, M., 1987 | MR | Zbl

[3] Ikramov Kh. D., Chugunov V. N., “Neskolko zamechanii o teplitsevykh i gankelevykh tsirkulyantakh”, Zapiski nauchnykh seminarov SPb otdeleniya akademii nauk, 334, Izd-vo Sankt-Peterburgskogo otdeleniya Matematicheskogo instituta im. V. A. Steklova RAN, SPb., 2006, 121–127 | MR | Zbl