Generic degeneracy of a non-hermitian hamiltonian implies a set of the eigenvectors is not enough to span the total linear space. One needs to extend the idea of the eigenstates to the generic ones, which we learn in linear algebra (Jordan cell decomposition). In this sense, the degeneracy of the non-hermitian hamiltonian is exceptional although it is generic. The minimal dimension of the Jordan cell is 2, which induces the simplest exceptional point (EP) for a momentum-dependent physical hamiltonian in 2 dimensions. It extends to the line if the hamiltonian respects some anti-unitary symmetry. The scenario can be generalized for multi-fold degeneracy. A threefold EP in two dimensions is protected by CP, which is realized in a shallow-water model, for example. The general scheme has been described with explicit topological invariants using resultant vectors in our recent paper, “Symmetry-protected multifold exceptional points and their topological characterization”, by Pierre Delplace, Tsuneya Yoshida, and Yasuhiro Hatsugai, accepted on Sep.8, 2021 and published in Phys. Rev. Lett. 127, 186602 – Published 25 October 2021. See also arXiv:2103.08232.