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