Geodesic
On the torsion in the general linear group and the diagonalization algorithm
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 55-71

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This work describes periodic matrices in the general linear group over the real numbers field and over the maximal Abelian extension $\mathbb{Q}_{\mathrm{ab}}$ of the rational numbers field. It is shown that for the case of real numbers the general question is reduced to the $2\times2$ matrices. A simple periodicity criterion is provided for them. We demonstrate a geometric interpretation of the results. The main result is an algorithm that tests periodicity of a matrix and, if the matrix is periodic, finds its Jordan form. 
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     title = {On the torsion in the general linear group and the diagonalization algorithm},
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A. V. Grishin; L. M. Tsybulya. On the torsion in the general linear group and the diagonalization algorithm. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2021) no. 4, pp. 55-71. http://geodesic.mathdoc.fr/item/FPM_2021_23_4_a3/