How to split the eigenvalues of a one-parameter family of matrices
Georg J. Still · Optimization · 2001
The paper is concerned with families F of n×n-matrices F(t) depending smoothly on the parameter . Firstly, a survey of results on the behavior of eigenvalues of fit for artain classes of matrices is given. Then 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 . A new natural type of perturbations of a given matrix family F is introduced such that lies in the. gcneric class. In other words, avoids double eigenvalues as far as possible according to the genexicity properties of the matrix class.