Definition 12.6.10 (Orthogonal Complement).label Let $H$ be an inner product space and $A \subset H$ be a subspace, then the closed subspace
\[A^{\perp} = \bracsn{x \in H| \dpn{x, y}{H} = 0 \forall y \in A}\]
is the orthogonal complement of $H$.
Definition 12.6.10 (Orthogonal Complement).label Let $H$ be an inner product space and $A \subset H$ be a subspace, then the closed subspace
is the orthogonal complement of $H$.
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