  Non-Hermiticity enables macroscopic accumulation of bulk states, named
non-Hermitian skin effects. The non-Hermitian skin effects are well-established
for single-particle systems, but their proper characterization for general
systems is elusive. Here, we propose a general criterion of non-Hermitian skin
effects, which works for any finite-dimensional system evolved by a linear
operator. The applicable systems include many-body systems and network systems.
A system meeting the criterion exhibits enhanced non-normality of the evolution
operator, accompanied by exceptional characteristics intrinsic to non-Hermitian
systems. Applying the criterion, we discover a new type of non-Hermitian skin
effect in many-body systems, which we dub the Fock space skin effect. We also
discuss the Fock space skin effect-induced slow dynamics, which gives an
experimental signal for the Fock space skin effect.
