  We characterize collections of orthogonal projections for which it is
possible to reconstruct a vector from the magnitudes of the corresponding
projections. As a result we are able to show that in an $M$-dimensional real
vector space a vector can be reconstructed from the magnitudes of its
projections onto a generic collection of $N \geq 2M-1$ subspaces. We also show
that this bound is sharp when $N = 2^k +1$. The results of this paper answer a
number of questions raised in \cite{CCPW:13}.
