  For an arbitrary possibly non-Hermitian matrix Hamiltonian H, that might
involve exceptional points, we construct an appropriate parameter space M and
the lines bundle L^n over M such that the adiabatic geometric phases associated
with the eigenstates of the initial Hamiltonian coincide with the holonomies of
L^n. We examine the case of 2 x 2 matrix Hamiltonians in detail and show that,
contrary to claims made in some recent publications, geometric phases arising
from encircling exceptional points are generally geometrical and not
topological in nature.
