- #1
buzzmath
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Homework Statement
Let P be a projection. The definition used is P is a projection if P = PP. Show that ||P|| >=1 with equality if and only if P is orthogonal.
Let ||.|| be the 2-norm
Homework Equations
P = PP. P is orthogonal if and only if P =P*
The Attempt at a Solution
I've proved the first part of ||P|| >= 1 and the first part of the equality portion. Assume P is orthogonal prove ||P|| = 1. However, I'm having a lot of trouble with the second part: Assume ||P|| = 1 show P is orthogonal.
Can someone point me in the right direction or suggest any ideas on how to use ||P|| = 1 to show that P = P*?
I've been playing around with inner products to try to solve this part but haven't gotten anything good out of it that uses the fact that ||P|| = 1