Special rank-one perturbations Original Research Article

The characteristic polynomial Δζ is given for a rank-one perturbation ζ = A − cbT in which A is square and f(A)c = 0 for some polynomial f(λ). This expression illustrates the exact way in which the factors of the polynomials Δζ 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 more general characterization of complete controllability for a single-input system, in terms of the λ-adjoint. In addition, this type of perturbation is used to generate a large class of simple matrix examples (possibly integer) with prescribed characteristic and minimal polynomials.