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Let $W\subset V$ be vector spaces. Is there exist a canonical way to construct a projector $\pi: V \to W$?

The same question for W is the kernel or image of some map.

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    It should be doable if you have an inner product.2012-07-20
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    Are they finite dimensional?2012-07-20
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    @copper.hat may be infinite2012-07-20
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    there is obvious way to do it not canonical in finite case2012-07-20
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    @Aspirin What you're thinking of probably works in the infinite case as well, but your choice of basis is going to matter.2012-07-20
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    Any continuity requirements?2012-07-20
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    @copper.hat no any requirements2012-07-20
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    I edited my question2012-07-20
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    $W$ is always a kernel of _some_ map [like $V \to V/W$], and the same goes for the image [$W \to V$].2012-07-20
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    You should make precise what you mean by *canonical*, as otherwise the question is pretty much unanswerable!2012-07-21

4 Answers 4