Froilán Dopico "Sets of matrix polynomials with bounded rank and degree and their generic eigenstructures"

Low rank perturbations of matrices, matrix pencils, and matrix polynomials appear naturally in many applications where just a few degrees of freedom of a complicated system are modifi ed. As a consequence many papers have been published in the last 15 years on this type of problems for matrices and pencils, but just a few for matrix polynomials. A possible reason of this lack of references on low rank perturbations of matrix polynomials is that the set of matrix polynomials with bounded (low) rank and  degree is not easy to describe explicitly when the rank is larger than one. The purpose of this talk is to describe such sets both in terms of its generic eigenstructures and in terms of products of two factors. We will consider mainly unstructured matrix polynomials but some results on structured ones will be also discussed.

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