## 2011.85: On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem

2011.85:
Yuji Nakatsukasa
(2011)
*On the condition numbers of a multiple eigenvalue
of a generalized eigenvalue problem.*

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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 diﬀerent 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 deﬁnite 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 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 65 Numerical analysis |

MIMS number: | 2011.85 |

Deposited By: | Yuji Nakatsukasa |

Deposited On: | 22 October 2011 |

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