Generalization of a solution to Sylvester matrix equation

Recently, a solution to the second-order Sylvester matrix equation was presented which did not depend on the Jordan form of a matrix F. Unfortunately, it was not shown some adequate schemes to calculation to the solution. In this paper, it will be shown that the idea can be used for the general-order equation. It will be also presented a calculation of minimal basis in polynomial vector space can be used for the solution to the general-order Sylvester matrix equation.