  Non-Hermitian skin effects and exceptional points are topological phenomena
characterized by integer winding numbers. In this study, we give methods to
theoretically detect skin effects and exceptional points by generalizing
inversion symmetry. The generalization is unique to non-Hermitian systems. We
show that parities of the winding numbers can be determined from energy
eigenvalues on the inversion-invariant momenta when generalized inversion
symmetry is present. The simple expressions for the winding numbers allow us to
easily analyze skin effects and exceptional points in non-Hermitian bands. We
also demonstrate the methods for (second-order) skin effects and exceptional
points by using lattice models.
