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

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Still, G.J. (1998) How to split the eigenvalues of a one-parameter family of matrices. [Report]

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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'.
Item Type:Report
Additional information:Imported from MEMORANDA
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65651
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