Conditions of Semiscalar Equivalence of One Class 3×3 Matrices of Simple Structure

This paper solves the problem of classifying matrices over a ring of polynomials up to semiscalarly equivalence transformations. For the selected set of polynomial matrices of simple structure, the so-called oriented by characteristic roots reduced matrix is constructed. The latter, in addition to the triangular form and the presence of invariant factors on the main diagonal, has some predefined properties. Invariants and conditions of semiscalar equivalence are established for such matrices.