The gap distance to the set of singular matrix pencils

Berger, Thomas GND; Gernandt, Hannes; Trunk, Carsten GND; Winkler, Henrik GND; Wojtylak, Michal GND

We study matrix pencils sE-A using the associated linear subspace ker[A,-E]. The distance between subspaces is measured in terms of the gap metric. In particular, we investigate the gap distance of a regular matrix pencil to the set of singular pencils and provide upper and lower bounds for it. A relation to the distance to singularity in the Frobenius norm is provided.

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Berger, T., Gernandt, H., Trunk, C., Winkler, H., Wojtylak, M., 2018. The gap distance to the set of singular matrix pencils.
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