English

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

Rings and Algebras 2024-04-01 v1

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.

Keywords

Cite

@article{arxiv.2403.19666,
  title  = {Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations},
  author = {Itziar Baragaña and Alicia Roca},
  journal= {arXiv preprint arXiv:2403.19666},
  year   = {2024}
}

Comments

17 pages. arXiv admin note: text overlap with arXiv:1907.10657