Evaluation of constituent matrices of a companion matrix with repeated eigenvalues

An analytical function of a companion matrix with repeated eigenvalues is expressed in terms of constituent matrices. The constituent matrices are then found to be equal to the product of two matrices with elements partly from a certain matrix and its inversion. This matrix may be either a Vandermonde matrix or a modal matrix. Equations for computing these matrices are given as a power series of x which is very useful for both hand and machine computations.