I was looking for some help on my math homework.
The question is, let $P=P_E$ be the matrix of an orthogonal projection onto a subspace E. Show that:
a. The matrix is self-adjoint, meaning A=A*
b. $P^2=P$
I just cannot really figure out where to start on both parts of these. Does anyone have any suggestions? I see how the properties are applied when looking at orthogonal projection matrices, I just cannot see where to go to start trying to prove it.