  Edidin [3] proved a fundamental result in phase retrieval: Theorem: A family
of orthogonal projections $\{P_i\}_{i=1}^m$ does phase retrieval in
$\mathbb{R}^n$ if and only if for every $0\not= x\in \mathbb{R}^n$, the family
$\{P_ix\}_{i=1}^m$ spans $\mathbb{R}^n$. The proof of this result relies on
Algebraic Geometry and so is inaccessible to many people in the field. We will
give an elementary proof of this result without Algebraic Geometry. We will
also solve the complex version of this result by showing that the "if" part
fails and the "only if" part holds in $\mathbb{C}^n$. Finally, we will show
that these techniques can be used to verify two classifications of norm
retrieval.
