Oriented by Characteristic Roots Reduced Matrices in the Class of Semiscalarly Equivalent

A set of polynomial 3x3-matrices of simple structure has been singled out, for which a so-called oriented by certain characteristic roots reduced matrix is established in the class of semiscalarly equivalent. The invariants of such reduced matrices and the conditions of their semiscalar equivalence are indicated. The obtained results will also be applied to the problem of similarity of sets of numerical matrices.