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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 3, Pages 85–88
DOI: https://doi.org/10.26907/0021-3446-2022-3-85-88 (Mi ivm9762) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

On some properties of sequences of traces of powers of matrices

A. N. Abyzov, M. M. Yamaleev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2022-3-85-88
Abstract: In this paper, we study sequences of the form $ \{\mathrm{tr}(A^k)\}_{k \in \mathbb {N}}, $ where $ A $ is a matrix with components from some field. For such sequences, the conditions for their periodicity are found, and the results from the works by A.M. Bikchentaev, P.N. Ivanshin (2021) and by S.O. Shatunovsky (1903) are obtained as corollaries.
Keywords: matrix, trace, eigenvalue, numerical sequence.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-882
Received: 22.12.2021
Revised: 22.12.2021
Accepted: 23.12.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 3, Pages 72–74
DOI: https://doi.org/10.3103/S1066369X2203001X
Document Type: Article
UDC: 512.643
Language: Russian
Citation: A. N. Abyzov, M. M. Yamaleev, “On some properties of sequences of traces of powers of matrices”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 3, 85–88; Russian Math. (Iz. VUZ), 66:3 (2022), 72–74
Citation in format AMSBIB
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\by A.~N.~Abyzov, M.~M.~Yamaleev
\paper On some properties of sequences of traces of powers of matrices
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 3
\pages 85--88
\mathnet{http://mi.mathnet.ru/ivm9762}
\crossref{https://doi.org/10.26907/0021-3446-2022-3-85-88}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 3
\pages 72--74
\crossref{https://doi.org/10.3103/S1066369X2203001X}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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