Geodesic
Similarity of matrices with integer spectra over the ring of integers
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 86-94

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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},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_3_a8/}
}
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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/