\begin{definition}[Definition:Orthogonal Difference]
Let $H$ be a Hilbert space.
Let $M, N$ be closed linear subspaces of $H$.
Then the '''orthogonal difference of $M$ and $N$''', denoted $M \ominus N$, is the set $M \cap N^\perp$.
It is in fact a closed linear subspace of $H$, as proven on Orthogonal Difference is Closed Linear Subspace.
\end{definition}