Technical report: Two observations on probability distribution   symmetries for randomly-projected data
  In this technical report, we will make two observations concerning symmetries of the probability distribution resulting from projection of a piece of p-dimensional data onto a random m-dimensional subspace of $\mathbb{R}^p$, where m < p. In particular, we shall observe that such distributions are unchanged by reflection across the original data vector and by rotation about the original data vector 
Hanchao Qi and Shannon M. Hughes
cs.IT math.IT