### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 1998 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1460 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-57Q65
- MSC-65F15
- EWI-3280
- IR-65651
- MSC-65H17

### Cite this

*How to split the eigenvalues of a one-parameter family of matrices*. Enschede: University of Twente, Department of Applied Mathematics.

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*How to split the eigenvalues of a one-parameter family of matrices*. University of Twente, Department of Applied Mathematics, Enschede.

**How to split the eigenvalues of a one-parameter family of matrices.** / Still, Georg J.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - How to split the eigenvalues of a one-parameter family of matrices

AU - Still, Georg J.

N1 - Imported from MEMORANDA

PY - 1998

Y1 - 1998

N2 - We are concerned with families $F$ of $n \times n$-matrices $F(t)$ depending smoothly on the parameter $ t \in \mathbb{R}$. We survey results on the behaviour of eigenvalues of $F(t)$ for certain classes of matrices. We are especially interested in the question whether multiple eigenvalues can be avoided generically. In the set of families of symmetric matrices $F(t)$, for example, generically all eigenvalues of $F(t)$ are simple for all $t \in \mathbb{R}$. We consider a class of natural perturbations $\widetilde{F}$ of a given matrix family $F$ such that $\widetilde{F}$ lies in the generic class, i.e.\ $\widetilde{F}$ avoids double eigenvalues `as far as possible'.

AB - We are concerned with families $F$ of $n \times n$-matrices $F(t)$ depending smoothly on the parameter $ t \in \mathbb{R}$. We survey results on the behaviour of eigenvalues of $F(t)$ for certain classes of matrices. We are especially interested in the question whether multiple eigenvalues can be avoided generically. In the set of families of symmetric matrices $F(t)$, for example, generically all eigenvalues of $F(t)$ are simple for all $t \in \mathbb{R}$. We consider a class of natural perturbations $\widetilde{F}$ of a given matrix family $F$ such that $\widetilde{F}$ lies in the generic class, i.e.\ $\widetilde{F}$ avoids double eigenvalues `as far as possible'.

KW - MSC-57Q65

KW - MSC-65F15

KW - EWI-3280

KW - IR-65651

KW - MSC-65H17

M3 - Report

BT - How to split the eigenvalues of a one-parameter family of matrices

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -