Derogatory exceptional points in non-Hermitian systems can be converted to non-derogatory exceptional points of the same order by infinitesimal perturbations, forming hierarchies of degeneracy structures both with and without pseudo-Hermitian symmetry.
Pseudo-Hermiticity versus PT symmetry: The necessary condition for the real- ity of the spectrum of a non-Hermitian Hamilto- nian,
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Converting non-Hermitian degeneracies of any order: Hierarchies of exceptional points and degeneracy manifolds
Derogatory exceptional points in non-Hermitian systems can be converted to non-derogatory exceptional points of the same order by infinitesimal perturbations, forming hierarchies of degeneracy structures both with and without pseudo-Hermitian symmetry.