Projection matrix and Eigenvalue Would like to have some guidance. $P$ is projection matrix on $U$ and $0\notin v\notin \mathbb{R}^2$
I need to show that if $v$ is element of $U$ than $v$ is Eigenvector of $P$ with Eigenvalue 1.
I know that for projection matrix Eigenvalue is $1$ or $0$... but why in this case only $1$?

Well here I think that you mean that if v in U than v is an eigenvector of P (you said A) with eigenvalue 1. I think all you need here is the fact that P is
(By definition projection ONTO U), so what happens to a v in U under the projection to U by P?... it projects it to itself. Ie if v is not 0 and v in U,
Pv = v!
