# Circled minus sign

## Main Question or Discussion Point

This should be really easy, but I can't seem to find the answer. What does the symbol $\ominus$ mean in the context of Hilbert spaces? As in "$H \ominus A$" where H is a Hilbert space and A is presumably a subspace or subset of H. I'm guessing it's like the inverse of a direct sum, $\oplus$? As in, if $H = A \oplus B$, then $H \ominus A = B$. Is that correct?

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Did some more searching and found the answer here. One of the answers there says:

If $A \subset B$ are linear subspaces of a Hilbert space, $B \ominus A = \{x \in B: (x,y) = 0 \text{ for all }y \in A\}$. $\ominus$ is also used for the symmetric difference of sets.

HallsofIvy
Thanks for posting that. So "$A\oplus B$" is the "orthogonal complement" of B in A.