  Recently, two different approaches were put forward to extend the
supersymmetry method in random matrix theory from Gaussian ensembles to general
rotation invariant ensembles. These approaches are the generalized
Hubbard-Stratonovich transformation and the superbosonization formula. Here, we
prove the equivalence of both approaches. To this end, we reduce integrals over
functions of supersymmetric Wishart-matrices to integrals over quadratic
supermatrices of certain symmetries.
