Note on the practical significance of the Drazin inverse

The solution of the differential system Bx = Ax + f where A and B are n x n matrices, and A - Lambda B is not a singular pencil, may be expressed in terms of the Drazin inverse. It is shown that there is a simple reduced form for the pencil A - Lambda B which is adequate for the determination of the general solution and that although the Drazin inverse could be determined efficiently from this reduced form it is inadvisable to do so.