Definition:Orthogonal Difference

This page is about Orthogonal Difference. For other uses, see Orthogonal.

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 $M \cap N^\perp$.

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Also see

• Orthogonal Difference is Closed Linear Subspace

Sources

• 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next) $\text {II}.3.4$