Factorization of the Partly Non-rational Matrix of Arbitrary Order

It is proposed a constructive method of factorization of partly non-rational matrix-functions of an arbitrary order. The algorithm is efficient for the case when columns or rows consist of rational functions. Our method generalizes the method of factorization of the triangular matrix function of an arbitrary order and the method of reduction of the matrix-function with a rational column/row to the triangular matrix-function.