Geodesic
On similarity classes of second order matrices with zero trace over the ring of integers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 79-86

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In this paper we consider the problem of similarity of matrices over integers and describe canonical representatives of the similarity classes of $2\times2$ matrices with zero trace and determinant equal to an odd power of a prime number.
Keywords: similarity of matrices, the ring of integers, canonical matrices. 
S. V. Sidorov. On similarity classes of second order matrices with zero trace over the ring of integers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2016), pp. 79-86. http://geodesic.mathdoc.fr/item/IVM_2016_4_a9/
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[1] Latimer C. G., MacDuffee C. C., “A correspondence between classes of ideals and classes of matrices”, Ann. Math., 34:2 (1933), 313–316 | DOI | MR | Zbl

[2] Taussky O., “On a theorem of Latimer and MacDuffee”, Canad. J. Math., 1 (1949), 300–302 | DOI | MR | Zbl

[3] Faddeev D. K., “Ob ekvivalentnosti sistem tselochislennykh matrits”, Izv. AN SSSR. Ser. matem., 30:2 (1966), 449–454 | MR | Zbl

[4] Grunewald F., “Solution of the conjugacy problem in certain arithmetic groups”, Word Problems, v. II, ed. Adian S. I., Boone W. W., Higman G., North-Holland, Amsterdam, 1980, 101–139 | DOI | MR

[5] Sarkisyan R. A., “Problema sopryazhennosti dlya naborov tselochislennykh matrits”, Matem. zametki, 25:6 (1979), 811–824 | MR | Zbl

[6] Sidorov S. V., “O podobii matrits s tselochislennym spektrom nad koltsom tselykh chisel”, Izv. vuzov. Matem., 2011, no. 3, 86–94 | MR | Zbl

[7] Shevchenko V. N., Sidorov S. V., “O podobii matrits vtorogo poryadka nad koltsom tselykh chisel”, Izv. vuzov. Matem., 2006, no. 4, 57–64 | MR | Zbl

[8] Appelgate H., Onishi H., “The similarity problem for $3\times3$ integer matrices”, Linear Algebra Appl., 42 (1982), 159–174 | DOI | MR | Zbl

[9] Sidorov S. V., “O podobii matrits tretego poryadka nad koltsom tselykh chisel, imeyuschikh privodimyi kharakteristicheskii mnogochlen”, Vestn. NNGU. Ser. matem. modelir. i optimal. upravlenie, 2009, no. 1, 119–127 | MR

[10] Lagarias J. C., “On the computational complexity of determining the solvability or unsolvability of the equation $X^2-DY^2=-1$”, Trans. Amer. Math. Soc., 260:2 (1980), 485–508 | MR | Zbl

[11] Ankeny N. C., Artin E., Chowla S., “The class-number of real quadratic number fields”, Ann. Math. Second Ser., 56:3 (1952), 479–493 | DOI | MR | Zbl