István Szöllősi (Cluj)

Combinatorics of Kronecker modules with applications to the matrix subpencil problem

Abstract:

We present some recent results concerning morphisms and short exact sequences in the category of Kronecker modules. We give numerical criteria for the existence of embeddings and projections between various types of Kronecker modules and also describe explicitly the middle terms in short exact sequences of preinjective (respectively preprojective) Kronecker modules, revealing some interesting combinatorial properties. Kronecker modules correspond to matrix pencils in linear algebra and we show how our results can lead to the explicit solution (in some special cases for now) of the matrix subpencil problem, an important open problem with applications in control theory and engineering. We compare our findings to other results from the theory of matrix pencils.