Department of Applied Mathematics, University of Twente
Abstract
We are concerned with families F of n×n-matrices F(t) depending smoothly on the parameter t∈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∈R. We consider a class of natural perturbations F of a given matrix family F such that F lies in the generic class, i.e.\ F avoids double eigenvalues `as far as possible'