Let A, i = 1, 2,...,n be n distinct eigenvalues of a matrix A C*** and let z and y be the corresponding right- and left-unit eigenvectors such that y = 1. Show that and 12 yxj=dij, A=Miriyi (Cri)(s; B) 8-A C(sI-A)-B= Furthermore, show that the mode A, is controllable iff y; B 0 and the mode A, is observable iff Ca #0.