Show that if A is a normal operator in an n-dimensional vector space, and if A has r distinct eigenvalues a1,a2,...ar, then the projection operator onto the subspace with eigenvalue ai can be written as:
A= (i=1 to r)[tex]\Sigma[/tex]aiPi
The Attempt at a Solution
First, sorry I'm a noob at text formatting.
The equations I put in are basically my attempt at the solution. They weren't included in the problem, but I was looking around and thought that they are appropriate. I really don't know where to start with this, and after staring at it for a good hour or so, I've decided to ask for direction.