# Orthogonal Projection

• December 7th 2011, 03:01 PM
problem
Orthogonal Projection
If E is a projection on V with range W and suppose $\|Ex\| \le \|x\|$ for all $x \in V$, prove that E is in fact an orthogonal projection on W.
• December 7th 2011, 04:30 PM
HallsofIvy
Re: Orthogonal Projection
If E is not orthogonal on W, then there exist some other subspace, U, such that E is orthogonal on U. Let x be a vector in U and show that ||Ex||> ||x||.