Low Rank Perturbation of Jordan Structure

@article{Moro2003LowRP,
  title={Low Rank Perturbation of Jordan Structure},
  author={J. Moro and F. Dopico},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2003},
  volume={25},
  pages={495-506}
}
  • J. Moro, F. Dopico
  • Published 2003
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
Let A be a matrix and $\lambda_0$ be one of its eigenvalues having g elementary Jordan blocks in the Jordan canonical form of A. We show that for most matrices B satisfying ${\rm rank}\,(B)\leq g$, the Jordan blocks of A+B with eigenvalue $\lambda_0$ are just the $g-{\rm rank}\,(B)$ smallest Jordan blocks of A with eigenvalue $\lambda_0$. The set of matrices for which this behavior does not happen is explicitly characterized through a scalar determinantal equation involving B and some of the… Expand
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