  We calculate the average of two characteristic polynomials for the real
Ginibre ensemble of asymmetric random matrices, and its chiral counterpart.
Considered as quadratic forms they determine a skew-symmetric kernel from which
all complex eigenvalue correlations can be derived. Our results are obtained in
a very simple fashion without going to an eigenvalue representation, and are
completely new in the chiral case. They hold for Gaussian ensembles which are
partly symmetric, with kernels given in terms of Hermite and Laguerre
polynomials respectively, depending on an asymmetry parameter. This allows us
to interpolate between the maximally asymmetric real Ginibre and the Gaussian
Orthogonal Ensemble, as well as their chiral counterparts.
