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On Some Properties in Sequences of Traces of Matrices’ Powers

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Abstract

In this paper, we study sequences of the form {tr(Ak)}k∈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 and P.N. Ivanshin (2021) and by S.O. Shatunovsky (1903) are obtained as corollaries.

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REFERENCES

  1. A. V. Zareula, “On congruences for the traces of powers of some matrices,” Proc. Steklov Inst. Math. 263, 78–98 (2008). https://doi.org/10.1134/S008154380804007X

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  2. A. M. Bikchentaev and P. N. Ivanshin, “On operators all of which powers have the same trace,” Int. J. Theor. Phys. 60 (2), 534–545 (2021). https://doi.org/10.1007/s10773-019-04059-x

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  3. S. O. Shatunovskii, On the Conditions for the Existence of n Unequal Roots of Congruence of the nth Degree Modulo a Prime (Tipo-Litografiya Imp. Univ., Kazan, 1903) [in Russian].

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Funding

This work is supported in part by the Program of Development of the Research and Educational Mathematical Center of the Volga Federal District, agreement no. 075-02-2022-882.

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Authors and Affiliations

  1. Kazan Federal University, 420008, Kazan, Russia

    A. N. Abyzov & M. M. Yamaleev

Authors
  1. A. N. Abyzov
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  2. M. M. Yamaleev
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Correspondence to A. N. Abyzov or M. M. Yamaleev.

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The authors declare that they have no conflicts of interest.

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Translated by E. Oborin

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Abyzov, A.N., Yamaleev, M.M. On Some Properties in Sequences of Traces of Matrices’ Powers. Russ Math. 66, 72–74 (2022). https://doi.org/10.3103/S1066369X2203001X

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  • DOI: https://doi.org/10.3103/S1066369X2203001X

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