Geodesic
Similarity of matrices with integer spectra over the ring of integers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 86-94 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider matrices with integer spectra whose Jordan forms contain no blocks of equal order for one and the same eigenvalue. We propose a quasipolynomial time algorithm for recognizing the similarity of such matrices over the ring of integers. In the case, when the algebraic multiplicity of all eigenvalues equals 1, we estimate the number of similarity classes.
Keywords: similarity of matrices, ring of integers, matrix spectrum.
Mots-clés : Jordan form 
@article{IVM_2011_3_a8,
     author = {S. V. Sidorov},
     title = {Similarity of matrices with integer spectra over the ring of integers},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {86--94},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_3_a8/}
}
TY  - JOUR
AU  - S. V. Sidorov
TI  - Similarity of matrices with integer spectra over the ring of integers
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 86
EP  - 94
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_3_a8/
LA  - ru
ID  - IVM_2011_3_a8
ER  - 
%0 Journal Article
%A S. V. Sidorov
%T Similarity of matrices with integer spectra over the ring of integers
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 86-94
%N 3
%U http://geodesic.mathdoc.fr/item/IVM_2011_3_a8/
%G ru
%F IVM_2011_3_a8
S. V. Sidorov. Similarity of matrices with integer spectra over the ring of integers. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 86-94. http://geodesic.mathdoc.fr/item/IVM_2011_3_a8/

[1] Maltsev A. I., Osnovy lineinoi algebry, Nauka, M., 1970

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

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

[4] Grunewald F., “Solution of the conjugacy problem in certain arithmetic groups”, Word problems, II, Stud. Logic Found. Math., 95, 1980, 101–139 | MR | Zbl

[5] Gantmakher F. R., Teoriya matrits, Fizmatlit, M., 2004