Definition:Orthogonal Difference

Definition
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.