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Non-Hermitian skin effect is a basic phenomenon in non-Hermitian system,which means that an extensive number of eigenstates can be localized at theboundary. In this Letter, we systematically investigate the constraints fromall internal symmetries on the non-Hermitian skin effect in arbitrarydimensions. By adopting the powerful Amoeba formulation, we build a genericcorrespondence between the various internal symmetries and the behavior of thenon-Hermitian skin effect. Notably, we find that, for non-Hermitian systemswith the time-reversal$^\dagger$ symmetry, the eigenstates can simultaneouslylocalize at opposite boundaries, which is beyond the Amoeba formulation, and wedub the phenomenon bidirectional skin effect. Our work provides an overallperspective from the internal symmetry to the non-Hermitian skin effect.

Constraints of Internal Symmetry on Non-Hermitian Skin Effect and Bidirectional Skin Effect Under Time-reversal$^\dagger$ Symmetry