This article is cited in 8 papers

On Some “Tame” and “Wild” Aspects of the Problem of Semiscalar Equivalence of Polynomial Matrices

B. Z. Shavarovskii

Ya. S. Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, NAS Ukraine

Abstract: The problem of reducing polynomial matrices to canonical form by using semiscalar equivalent transformations is studied. This problem is wild as a whole. However, it is tame in some special cases. In the paper, classes of polynomial matrices are singled out for which canonical forms with respect to semiscalar equivalence are indicated. We use this tool to construct a canonical form for the families of coefficients corresponding to the polynomial matrices. This form enables one to solve the classification problem for families of numerical matrices up to similarity.

UDC: 512.64

Received: 30.09.2002
Revised: 16.04.2003

DOI: 10.4213/mzm94

 English version: Mathematical Notes, 2004, 76:1, 111–123

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