  We study the skin effect in a one-dimensional system of finitely many
subwavelength resonators with a non-Hermitian imaginary gauge potential. Using
Toeplitz matrix theory, we prove the condensation of bulk eigenmodes at one of
the edges of the system. By introducing a generalised (complex) Brillouin zone,
we can compute spectral bands of the associated infinitely periodic structure
and prove that this is the limit of the spectra of the finite structures with
arbitrarily large size. Finally, we contrast the non-Hermitian systems with
imaginary gauge potentials considered here with systems where the
non-Hermiticity arises due to complex material parameters, showing that the two
systems are fundamentally distinct.
