V is vector space P:V-->V

linear transformation witch is projection, P=P^2.

PROVE:

1. For every x in V: x in Im(P) <==> x=Px

2. Let suppose that V is inner product space and P orthogonal projection. (*)

Prove ||x|| >= ||Px||

def. of orthogonal projection:

x-Px in (ImP)^# for all x in V.

# is orthogonal sign.