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Sib. Zh. Vychisl. Mat., 2017, Volume 20, Number 4, Pages 439–444 (Mi sjvm662)  

A description of pairs of the quasi-commuting Toeplitz and Hankel matrices

V. N. Chugunova, Kh. D. Ikramovb

a Institute of Numerical Mathematics, Russian Academy of Sciences, 8 Gubkina str., Moscow, 119333, Russia
b Lomonosov Moscow State University, GSP-1 Leninskie Gory, Moscow, 119991, Russia

Abstract: We say that the square matrices $A$ and $B$ are of the same order quasi-commute if $AB=\sigma BA$ for some scalar $\sigma$. Classical relations of commutation and anti-commutation are particular cases of this definition. We give a complete description of pairs of the quasi-commuting Toeplitz and Hankel matrices for $\sigma\ne\pm1$.

Key words: Toeplitz matrix, Hankel matrix, $\phi$-circulant, quasi-commuting matrices.

Funding Agency Grant Number
Russian Science Foundation 14-11-00806


DOI: https://doi.org/10.15372/SJNM20170407

Full text: PDF file (430 kB)
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English version:
Numerical Analysis and Applications, 2017, 10:4, 358–361

Bibliographic databases:

UDC: 512.643
Received: 27.02.2017
Revised: 19.04.2017

Citation: V. N. Chugunov, Kh. D. Ikramov, “A description of pairs of the quasi-commuting Toeplitz and Hankel matrices”, Sib. Zh. Vychisl. Mat., 20:4 (2017), 439–444; Num. Anal. Appl., 10:4 (2017), 358–361

Citation in format AMSBIB
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\paper A description of pairs of the quasi-commuting Toeplitz and Hankel matrices
\jour Sib. Zh. Vychisl. Mat.
\yr 2017
\vol 20
\issue 4
\pages 439--444
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\crossref{https://doi.org/10.15372/SJNM20170407}
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\jour Num. Anal. Appl.
\yr 2017
\vol 10
\issue 4
\pages 358--361
\crossref{https://doi.org/10.1134/S1995423917040073}
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