Question

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?

Answer 1

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))

Answer 2

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?

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

K