Geodesic
Classification of real pairs of commuting Toeplitz and Hankel matrices
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 457-467 
V. N. Chugunov; Kh. D. Ikramov. Classification of real pairs of commuting Toeplitz and Hankel matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 19 (2016) no. 4, pp. 457-467. http://geodesic.mathdoc.fr/item/SJVM_2016_19_4_a8/
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     title = {Classification of real pairs of commuting {Toeplitz} and {Hankel} matrices},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We give a complete description of the set of matrix pairs such that $T$ is a real Toeplitz matrix, $H$ is a real Hankel matrix, and $TH=HT$.

[1] Gelfgat V. I., “Usloviya kommutirovaniya teplitsevykh matrits”, Zhurn. vychisl. matem. i mat. fiziki, 38:1 (1998), 11–14 | MR | Zbl

[2] Ikramov Kh. D., Chugunov V. N., “Kriterii normalnosti kompleksnoi teplitsevoi matritsy”, Zhurn. vychisl. matem. i mat. fiziki, 36:2 (1996), 3–10 | MR | Zbl

[3] Farenick D. R., Krupnik M., Krupnik N., Lee W. Y., “Normal Toeplitz matrices”, SIAM J. Matrix Anal. Appl., 17:4 (1996), 1037–1043 | DOI | MR | Zbl

[4] Ito K., “Every normal Toeplitz matrix is either of type I or of type II”, SIAM J. Matrix Anal. Appl., 17:4 (1996), 998–1006 | DOI | MR | Zbl

[5] Arimoto A., “A simple proof of the classification of normal Toeplitz matrices”, Electronic J. Linear Algebra, 9 (2002), 108–111 | DOI | MR | Zbl

[6] Gu G., Patton L., “Commutation relations for Toeplitz and Hankel matrices”, SIAM J. Matrix Anal. Appl., 24 (2003), 728–746 | DOI | MR | Zbl

[7] Ikramov Kh. D., Chugunov V. N., “O kososimmetrichnoi chasti proizvedeniya teplitsevykh matrits”, Mat. zametki, 63:1 (1998), 138–141 | DOI | MR | Zbl

[8] Ikramov Kh. D., Chugunov V. N., “O normalnykh gankelevykh matritsakh”, Zapiski nauchnykh seminarov POMI im. V. A. Steklova Rossiiskoi akademii nauk, 346, 2007, 63–80 | MR

[9] Ikramov Kh. D., Chugunov V. N., “O svedenii normalnoi gankelevoi zadachi k dvum chastnym sluchayam”, Mat. zametki, 85:5 (2009), 768–781 | DOI | MR | Zbl

[10] Chugunov V. N., “O dvukh chastnykh sluchayakh resheniya normalnoi gankelevoi zadachi”, Zhurn. vychisl. matem. i mat. fiziki, 49:6 (2009), 931–939 | MR | Zbl

[11] Chugunov V. N., Ikramov Kh. D., “A contribution to the normal Hankel problem”, Linear Algebra Appl., 430:8–9 (2009), 2094–2101 | DOI | MR | Zbl

[12] Chugunov V. N., Ikramov Kh. D., “A complete solution of the normal Hankel problem”, Linear Algebra Appl., 432:12 (2010), 3210–3230 | DOI | MR | Zbl

[13] Gelfgat V. I., “Usloviya kommutirovaniya gankelevykh matrits”, Zhurn. vychisl. matem. i mat. fiziki, 51:7 (2011), 1181–1193 | MR | Zbl

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

[15] Chugunov V. N., Ikramov Kh. D., “Permutability of Toeplitz and Hankel matrices”, Linear Algebra Appl., 467 (2015), 226–242 | DOI | MR | Zbl

[16] Chugunov V. N., Ikramov Kh. D., “A complete solution of the permutability problem for Toeplitz and Hankel matrices”, Linear Algebra Appl., 478 (2015), 53–80 | DOI | MR | Zbl

[17] Chugunov V. N., Ikramov Kh. D., “O klassifikatsii par perestanovochnykh teplitsevoi i gankelevoi matrits”, Doklady RAN, 464:4 (2015), 406–410 | DOI | MR | Zbl

[18] Chugunov V. N., “O parametrizatsii klassov normalnykh gankelevykh matrits”, Zhurn. vychisl. matem. i mat. fiziki, 51:11 (2011), 1939–1951 | MR | Zbl