Let and for :

.

For any , find its projection on .

I have no idea where to start. I know that the projection map has certain properties (linear, self-adjoint, operator norm of 1, whatever), but is there any specific formula to find it?

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- Nov 30th 2010, 09:01 AMmathematicalbagpiperProjection On L2 Space
Let and for :

.

For any , find its projection on .

I have no idea where to start. I know that the projection map has certain properties (linear, self-adjoint, operator norm of 1, whatever), but is there any specific formula to find it? - Nov 30th 2010, 09:31 AMAckbeet
Hmm. Interesting problem. The trick is that applying the projection operator twice should be the same as applying it just once . Couldn't you multiply each by the scalar

So,