Proximity of degeneracies and chiral points

For complex 2 x 2 matrices M, points of degeneracy (D), and chiral points (C) where the eigenvectors are circularly polarized, coincide when M is symmetric, and often lie close together when M is not symmetric. This proximity is explained statistically, by averaging over an ensemble in which the elements of M are random complex numbers: the standard deviation of the separation between C and D points is less than half the separation of the two D points. If the departure from symmetry is treated as a perturbation of strength e, the separation between C and D points is of order epsilon(2); the probability distribution of the separation is calculated.