A group theory rule for predicting eigenvalue crossings in characteristic mode analyses

The von Neumann-Wigner theorem is used to demonstrate the general result that objects without inherent geometric symmetry will have entirely noncrossing characteristic mode eigenvalues. This suggests that objects of this kind can be analyzed without the need of advanced eigenvalue tracking routines, save for special treatment of modes that numerically appear and disappear from the spectrum. Asymmetry introduced by meshing is examined, along with the convergence and lack of convergence of certain parameters related to symmetry with mesh refinement.