  We consider conditions for the existence of boundary modes in non-Hermitian
systems with edges of arbitrary co-dimension. Through a universal formulation
of formation criteria for boundary modes in terms of local Green functions, we
outline a generic perspective on the appearance of such modes and generate
corresponding dispersion relations. In the process, we explain the skin effect
in both topological and non-topological systems, exhaustively generalizing
bulk-boundary correspondence in the presence of non-Hermiticity. This is
accomplished via a doubled Green's function, inspired by doubled Hamiltonian
methods used to classify Floquet and, more recently, non-Hermitian topological
phases. Our work constitutes a general tool, as well as, a unifying perspective
for this rapidly evolving field. Indeed, as a concrete application we find that
our method can expose novel non-Hermitian topological regimes beyond the reach
of previous methods.
