Initial conditions, controllability, and Wronski relations

In recent letters, Stanley[1], Reis[2], and Fielder[3] investigated a matrix which related the numerator coefficients of a rational Laplace transform to the initial values of the inverse transform. In another letter, Silverman[4] had occasion to consider the controllability matrix of a linear dynamic system in canonic form. The present letter has two purposes. The first is to show that these two matrices are identical. The second is to solve the problem, once again, by use of Wronski relations,[5] thereby obtaining an easily computed solution to the problem in terms of eigenvalues.