  We establish a transcendental generalization of Nakamaye's theorem to compact
complex manifolds when the form is not assumed to be closed. We apply the
recent analytic technique developed by Collins--Tosatti to show that the
non-Hermitian locus of a nef and big $(1,1)$-form, which is not necessarily
closed, on a compact complex manifold equals the union of all
positive-dimensional analytic subvarieties where the restriction of the form is
not big (null locus). As an application, we can give an alternative proof of
the Nakai--Moishezon criterion of Buchdahl and Lamari for complex surfaces and
generalize this result in higher dimensions. This is also used for studying
degenerate complex Monge--Amp\`ere equations on compact Hermitian manifolds.
Finally, we investigate finite time non-collapsing singularities of the
Chern--Ricci flow, partially answering a question raised by Tosatti and
Weinkove.
