Remark 2

When the $b_j$ are all zero, that is, if the system (47) is homogeneous, the conditions (52) are always satisfied; if, further, $r = n$, one sees that the set of solutions of (47) is a vector space over $\mathbf{C}$, of dimension equal to the sum of the degrees of the $f_j(D)$, that is, to the degree of $\det(P(D))$.