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- anonymous

In this page: http://en.wikipedia.org/wiki/Projection_(linear_algebra)#cite_note-0
(and in my book)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that P^2 = P
What is the meaning of P^2 here?

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- anonymous

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- anonymous

No sure what u mean, isn't it just as it says at the top of
http://en.wikipedia.org/wiki/Projection_(linear_algebra)
ie P^2 = P(P(v))

- anonymous

I don't mean anything, I'm asking what is meant by it. It might be what you claim, but how is this operation called (at first I thought it was cartesian product or something), and where do you see it at the top?

- anonymous

Here http://en.wikipedia.org/wiki/Projection_(linear_algebra)#Simple_example

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- anonymous

I found what is meant by it: http://en.wikipedia.org/wiki/Function_composition

- anonymous

P(P(v)) IS function composition....:-)

- phi

P is a projection matrix.
if you have a vector x
Px will give you a vector in some subspace.
if x is already in that subspace then you would get x= Px
if we sub n Px for x in the equation x=Px we get x= PPx
from which we see Px= PPx or P= P^2

- anonymous

@ estudier yeah it's a function composition but you didn't tell me what it was called at first :)

- anonymous

True, you didn't ask for that, though, u asked for the meaning...

- anonymous

I did ask for it, but it's no problem really :D

- anonymous

K

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