  A regular matrix pencil sE-A and its rank one perturbations are considered.
We determine the sets in the extended complex plane which are the eigenvalues
of the perturbed pencil. We show that the largest Jordan chains at each
eigenvalue of sE-A may disappear and the sum of the length of all destroyed
Jordan chains is the number of eigenvalues (counted with multiplicities) which
can be placed arbitrarily in the extended complex plane. We prove sharp upper
and lower bounds of the change of the algebraic and geometric multiplicity of
an eigenvalue under rank one perturbations. Finally we apply our results to a
pole placement problem for a single-input differential algebraic equation with
feedback.
