This article is cited in 6 papers

Similarity of matrices with integer spectra over the ring of integers

S. V. Sidorov

Chair of Mathematical Logic and Higher Algebra, Nizhni Novgorod State University, Nizhni Novgorod, Russia

Abstract: 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, Jordan form, matrix spectrum.

UDC: 512.64

Received: 17.09.2009
Revised: 02.11.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:3, 77–84

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