SPECIAL RANK-ONE PERTURBATIONS

The characteristic polynomial Delta(lambda) is given for a rank-one pe rturbation zeta = A - cb(T) in which A is square and f(A)c = 0 for som e polynomial f(lambda). This expression illustrates the exact way in w hich the factors of the polynomials Delta(zeta) and f are interchanged . For the minimal polynomial the same is done for the case where f is linear. This type of perturbation is then used to obtain a slightly mo re general characterization of complete controllability for a single-i nput system, in terms of the lambda-adjoint. In addition, this type of perturbation is used to generate a large class of simple matrix examp les (possibly integer) with prescribed characteristic and minimal poly nomials.