Definition 12.6.9 (Orthogonal Projection).label Let $H$ be an inner product space and $P \in L(H; H)$, then $P$ is an orthogonal projection if:
- (1)
$P$ is idempotent.
- (2)
For any $x, y \in H$, $\dpn{Px, y}{H}= \dpn{x, Py}{H}$.
Definition 12.6.9 (Orthogonal Projection).label Let $H$ be an inner product space and $P \in L(H; H)$, then $P$ is an orthogonal projection if:
$P$ is idempotent.
For any $x, y \in H$, $\dpn{Px, y}{H}= \dpn{x, Py}{H}$.
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