  We are interested in the distribution of Wishart samples after forgetting
their scaling factors. We call such a distribution a projective Wishart
distribution. We show that projective Wishart distributions have strong links
with the affine-invariant geometry of symmetric positive definite matrices in
the real case or Hermitian positive definite matrices in the complex case.
First, the Fr{\'e}chet mean of a projective Wishart distribution is the
covariance parameter, up to a scaling factor, of the corresponding Wishart
distribution. Second, in the case of 2 by 2 matrices, the densities have simple
expressions in term of the affine-invariant distance.
