The quasi-Kronecker form for matrix pencils

Berger, Thomas GND; Trenn, Stephan GND

We study singular matrix pencils and show that the so called Wong sequences yield a quasi-Kronecker form. This form decouples the matrix pencil into an underdetermined part, a regular part and an overdetermined part. This decoupling is sufficient to fully characterize the solution behaviour of the differential-algebraic equations associated with the matrix pencil. Furthermore, the Kronecker canonical form is a simple corollary of our result, hence, in passing by, we also provide a new proof for the Kronecker canonical form. The results are illustrated with an example given by a simple electrical circuit.

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Berger, Thomas / Trenn, Stephan: The quasi-Kronecker form for matrix pencils. 2011.

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