Projective Hilbert space structures at exceptional points

@article{Gnther2007ProjectiveHS,
  title={Projective Hilbert space structures at exceptional points},
  author={Uwe G{\"u}nther and Ingrid Rotter and Boris F. Samsonov},
  journal={Journal of Physics A},
  year={2007},
  volume={40},
  pages={8815-8833}
}
A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseuxexpanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behaviour in the EP-limit can be resolved by projectively extending the original Hilbert space. The… 
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