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Projection operator in spectrum theory

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Homework Statement



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:

Pi=[(A-a1)...(A-aa-1)...(A-ar)]/[(ai-a1) ...(ai-ai-1)...(ai-ai+1)...(a1-ar)]


Homework Equations



APiz=aiPiz

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.
 

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