  The theory of zonal polynomials is used to compute the average of a Schur
polynomial of argument $AX$, where $A$ is a fixed matrix and $X$ is from the
real Ginibre ensemble. This generalizes a recent result of Sommers and
Khorozhenko [J. Phys. A {\bf 42} (2009), 222002], and furthermore allows
analogous results to be obtained for the complex and real quaternion Ginibre
ensembles. As applications, the positive integer moments of the general
variance Ginibre ensembles are computed in terms of generalized hypergeometric
functions, these are written in terms of averages over matrices of the same
size as the moment to give duality formulas, and the averages of the power sums
of the eigenvalues are expressed as finite sums of zonal polynomials.
