The change of similarity invariants under row perturbations: Generic cases

The problem of characterizing the possible invariant factors or Weyr characteristic of all the matrices that can be obtained from a specified one by perturbing some of its rows is considered. Such a characterization is attained in two generic cases: first when the fixed submatrix form a completely controllable pair and second, for the noncontrollable case when a significant invariant subspace is cyclic.