Exceptional points and double poles of the S matrix.

Exceptional points and double poles of the S matrix are both characterized by the coalescence of a pair of eigenvalues. In the first case, the coalescence causes a defect of the Hilbert space. In the second case, this is not so as shown in previous papers. Mathematically, the reason for this difference is the biorthogonality of the eigenfunctions of a non-Hermitian operator that is ignored in the first case. The consequences for the topological structure of the Hilbert space are studied and compared with existing experimental data.