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

Georg J. Still

Research output: Book/ReportReportOther research output

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Abstract

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'.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Publication statusPublished - 1998

Publication series

Name
PublisherDepartment 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

Still, G. J. (1998). How to split the eigenvalues of a one-parameter family of matrices. Enschede: University of Twente, Department of Applied Mathematics.
Still, Georg J. / How to split the eigenvalues of a one-parameter family of matrices. Enschede : University of Twente, Department of Applied Mathematics, 1998.
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Still, GJ 1998, 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.

Enschede : University of Twente, Department of Applied Mathematics, 1998.

Research output: Book/ReportReportOther research output

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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

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Still GJ. How to split the eigenvalues of a one-parameter family of matrices. Enschede: University of Twente, Department of Applied Mathematics, 1998.