  The topology of non-Hermitian systems is drastically shaped by the
non-Hermitian skin effect, which leads to the generalized bulk-boundary
correspondence and non-Bloch band theory. The essential part in formulations of
bulk-boundary correspondence is a general and computable definition of
topological invariants. In this paper, we introduce a construction of
non-Hermitian topological invariants based directly on real-space
wavefunctions, which provides a general and straightforward approach for
determining non-Hermitian topology. As an illustration, we apply this
formulation to several representative models of non-Hermitian systems,
efficiently obtaining their topological invariants in the presence of
non-Hermitian skin effect. Our formulation also provides a dual picture of the
non-Bloch band theory based on the generalized Brillouin zone, offering a
unique perspective of bulk-boundary correspondence.
