Low Rank Perturbation of Weierstrass Structure

@article{Tern2008LowRP,
  title={Low Rank Perturbation of Weierstrass Structure},
  author={F. Ter{\'a}n and F. M. Dopico and J. Moro},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2008},
  volume={30},
  pages={538-547}
}
Let $A_0 + \lambda A_1$ be a regular matrix pencil, and let $\lambda_0$ be one of its finite eigenvalues having $g$ elementary Jordan blocks in the Weierstrass canonical form. We show that for most matrices $B_0$ and $B_1$ with ${\rm rank} (B_0 + \lambda_0 B_1)< g$ there are $g - {\rm rank} (B_0 + \lambda_0 B_1)$ Jordan blocks corresponding to the eigenvalue $\lambda_0$ in the Weierstrass form of the perturbed pencil $A_0+B_0 + \lambda (A_1+B_1)$. If ${\rm rank} (B_0 + \lambda_0 B_1)+ {\rm rank… Expand
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