Exceptional points of non-Hermitian operators

Exceptional points associated with non-Hermitian operators, i.e. operators being non-Hermitian for real parameter values, are investigated. The specific characteristics of the eigenfunctions at the exceptional point are worked out. Within the domain of real parameters the exceptional points are the points where eigenvalues switch from real to complex values. These and other results are exemplified by a classical problem leading to exceptional points of a non-Hermitian matrix.