Special rank-one perturbations
The characteristic polynomial \(\Delta_\zeta\) is given for a rank-one perturbation \(\xi =A-cb^T\) in which \(A\) is square and \(f(A)c = 0\) for some polynomial \(f (\lambda)\). 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 \(\lambda\)-adjoint. Also, this type of perturbation is used to generate a large class of simple matrix examples (possibly integer) with prescribed characteristic and minimal polynomials.
scientific article; zbMATH DE number 871119