Geodesic
On diagonalization of matrices in an arbitrary field
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 233-239.

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The paper presents a simple way for diagonalization of matrices in an arbitrary field, with which one can calculate functions of matrices. 
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V. D. Shmatkov. On diagonalization of matrices in an arbitrary field. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 233-239. http://geodesic.mathdoc.fr/item/FPM_2016_21_3_a13/

[1] Gantmakher F. R., Teoriya matrits, Nauka, M., 1967 | MR

[2] Lankaster P., Teoriya matrits, Nauka, M., 1970 | MR

[3] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR