Definition 12.6.8 (Orthogonal).label Let $H$ be an inner product space and $x, y \in H$, then $x$ and $y$ are orthogonal, denoted $x \perp y$, if $\dpn{x, y}{H}= 0$.

For any $A \subset H$, $A$ is pairwise orthogonal if for any $x, y \in A$, $x \perp y$.