## xcrypt 3 years ago 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?

1. estudier

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))

2. xcrypt

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?

3. estudier
4. xcrypt

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

5. estudier

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

6. 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

7. xcrypt

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

8. estudier

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

9. xcrypt

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

10. estudier

K