István Szöllősi "The matrix subpencil problem via Kronecker modules"

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. Kronecker modules correspond to matrix pencils and the matrix subpencil problem may be formulated in terms of the so-called extension monoid product of Kronecker modules. Therefore, studying the interesting combinatorics of the extension monoid product can lead to the complete, explicit solution of the matrix subpencil problem, with some new perspectives and insights.

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