Geodesic
On some properties of sequences of traces of powers of matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 85-88.

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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.
Mots-clés : matrix
Keywords: trace, eigenvalue, numerical sequence. 
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A. N. Abyzov; M. M. Yamaleev. On some properties of sequences of traces of powers of matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 85-88. http://geodesic.mathdoc.fr/item/IVM_2022_3_a8/

[1] Zarelua A. V., “O sravneniyakh dlya sledov stepenei nekotorykh matrits”, Tr. MIAN, 263, 2008, 85–105 | Zbl

[2] Bikchentaev A. M., Ivanshin P. N., “On Operators all of Which Powers have the same Trace”, Int. J. Theor. Phys., 60:2 (2021), 534–545 | DOI | MR | Zbl

[3] Shatunovskii S. O., Ob' usloviyakh' suschestvovaniya $n$ neravnykh' kornei sravneniya $n$-i stepeni po prostomu modulyu, Tipo-litografiya Imperatorsk. un-ta, Kazan, 1903