(adsbygoogle = window.adsbygoogle || []).push({}); 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 a_{1},a_{2},...a_{r}, then the projection operator onto the subspace with eigenvalue a_{i}can be written as:

P_{i}=[(A-a_{1})...(A-a_{a-1})...(A-a_{r})]/[(a_{i}-a_{1}) ...(a_{i}-a_{i-1})...(a_{i}-a_{i+1})...(a_{1}-a_{r})]

2. Relevant equations

AP_{i}z=a_{i}P_{i}z

A= (i=1 to r)[tex]\Sigma[/tex]a_{i}P_{i}

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.

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# Projection operator in spectrum theory

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