Geodesic
Pairs of symmetric and skew-symmetric Toeplitz matrices whose squares coincide
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 193-203 Cet article a éte moissonné depuis la source Math-Net.Ru

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A description of some sets of pairs of symmetric and skew-symmetric Toeplitz matrices whose squares coincide is provided. 
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     title = {Pairs of symmetric and skew-symmetric {Toeplitz} matrices whose squares coincide},
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V. N. Chugunov. Pairs of symmetric and skew-symmetric Toeplitz matrices whose squares coincide. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXV, Tome 514 (2022), pp. 193-203. http://geodesic.mathdoc.fr/item/ZNSL_2022_514_a10/

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

[2] V. H. Chugunov, Normalnye i perestanovochnye teplitsevy i gankelevy matritsy, Nauka, M., 2017

[3] N. V. Efimov, E. R. Rozendorn, Lineinaya algebra i mnogomernaya geometriya, Nauka, M., 1975