Nakatsukasa, Yuji
(2011)
*On the condition numbers of a multiple eigenvalue
of a generalized eigenvalue problem.*
[MIMS Preprint]

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## Abstract

For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take diï¬�erent values in the non-Hermitian case. We consider the generalized eigenvalue problem and identify the condition numbers. Our main result is that a multiple eigenvalue generally has multiple condition numbers, even in the Hermitian deï¬�nite case. The condition numbers are characterized in terms of the singular values of the outer product of the corresponding left and right eigenvectors.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | multiple eigenvalue, generalized eigenvalue problem, condition number |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis |

Depositing User: | Yuji Nakatsukasa |

Date Deposited: | 22 Oct 2011 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1689 |

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