If E is a projection on V with range W and suppose for all , prove that E is in fact an orthogonal projection on W.

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- December 7th 2011, 03:01 PMproblemOrthogonal Projection
If E is a projection on V with range W and suppose for all , prove that E is in fact an orthogonal projection on W.

- December 7th 2011, 04:30 PMHallsofIvyRe: 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||.