Definition:Projection (Hilbert Spaces)

From ProofWiki
Jump to navigation Jump to search

This page is about Projection in the context of Hilbert Space. For other uses, see Projection.


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:

$\ker P = \paren {\Img P}^\perp$


$\ker P$ denotes the kernel of $P$
$\Img P$ denotes the image of $P$
$\perp$ denotes orthocomplementation.

Also see