@book{ac054b03020945708ed85e562b68d486,

title = "How to split the eigenvalues of a one-parameter family of matrices",

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'.",

keywords = "MSC-57Q65, MSC-65F15, EWI-3280, IR-65651, MSC-65H17",

author = "Still, {Georg J.}",

note = "Imported from MEMORANDA",

year = "1998",

language = "Undefined",

publisher = "University of Twente, Department of Applied Mathematics",

number = "1460",

}