# Homework Help: Projection operator in spectrum theory

1. Feb 10, 2009

### seek

1. The problem statement, all variables and given/known data

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)]

2. Relevant equations

APiz=aiPiz

A= (i=1 to r)$$\Sigma$$aiPi

3. 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.