Definition:Projection (Hilbert Spaces)
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This page is about Projection in the context of Hilbert Space. For other uses, see Projection.
Definition
Let $H$ be a Hilbert space.
Let $P \in \map B H$ be an idempotent operator.
Then $P$ is said to be a projection if and only if:
- $\ker P = \paren {\Img P}^\perp$
where:
- $\ker P$ denotes the kernel of $P$
- $\Img P$ denotes the image of $P$
- $\perp$ denotes orthocomplementation.
Also see
Sources
- 1990: John B. Conway: A Course in Functional Analysis (2nd ed.) ... (previous) ... (next) $II.3.1$