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arXiv · 2403.19666

Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations

Itziar Baragaña·Alicia Roca
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Abstract

We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements.

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Itziar Baragaña, Alicia Roca. 2024-02-09. Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations. https://doi.org/10.1137/18m1200245

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