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.