GENERIC MOVEMENT OF EIGENVALUES FOR EQUIVARIANT SELF-ADJOINT MATRICES

In the numerical treatment of bifurcation problems one of the main tasks is to control the spectrum of matrices in a parametrized family. If the original problem possesses symmetry, then the matrices are additionally equivariant. Previously the generic eigenvalue behavior in a one-parameter family of equivariant matrices has been studied for the case of general matrices (Golubitsky et al., 1988) and for infinitesimally symplectic matrices (Dellnitz et al., 1992). However, in applications the situation frequently occurs that the matrices of the family are self-adjoint. We classify the generic eigenvalue in such a family of equivariant matrices by the type of underlying symmetry.