On perturbations and the equivalence orbit of a matrix pencil (Q1080918)

Two theorems on the canonical Kronecker form of a perturbed pencil are stated. These theorems are obtained using simple tensor calculus. The application of this calculus to matrix pencils resembles in some ways the application of the functional calculus to operators. It is shown also that theorems on perturbations of matrix pencils are in some sense the best possible. This aim is achieved by describing the closure of the equivalence orbit of a matrix pencil. This last concept is analogous to the concept of the similarity orbit of an operator.