### Abstract

We show that if an n X n Jordan block is perturbed by an O(ε) upper k-Hessenberg matrix (k subdiagonals including the main diagonal), then generically the eigenvalues split into p rings of size k and one of size r (if r ≠ 0), where n = pk + r. This generalizes the familiar result (k = n, p = 1, r = 0) that generically the eigenvalues split into a ring of size n. We compute the radii of the rings to first order and generalize the result in a number of directions involving multiple Jordan blocks of the same size.

Original language | English (US) |
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Pages (from-to) | 45-63 |

Number of pages | 19 |

Journal | Linear Algebra and Its Applications |

Volume | 273 |

Issue number | 1-3 |

DOIs | |

State | Published - Apr 1 1998 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

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## Cite this

Ma, Y., & Edelman, A. (1998). Nongeneric eigenvalue perturbations of Jordan blocks.

*Linear Algebra and Its Applications*,*273*(1-3), 45-63. https://doi.org/10.1016/S0024-3795(97)00342-X