  Issues in modal tracking in the presence of crossings and crossing avoidances
between eigenvalue traces are solved via the theory of point groups. The von
Neumann-Wigner theorem is used as a key factor in predictively determining mode
behavior over arbitrary frequency ranges. The implementation and capabilities
of the proposed procedure are demonstrated using characteristic mode
decomposition as a motivating example. The procedure is, nevertheless, general
and can be applied to an arbitrarily parametrized eigenvalue problems. A
treatment of modal degeneracies is included and several examples are presented
to illustrate modal tracking improvements and the immediate consequences of
improper modal tracking. An approach leveraging a symmetry-adapted basis to
accelerate computation is also discussed. A relationship between geometrical
and physical symmetries is demonstrated on a practical example.
