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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 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})]

## Homework Equations

AP

_{i}

**z**=a

_{i}P

_{i}

**z**

A= (i=1 to r)[tex]\Sigma[/tex]a

_{i}P

_{i}

## 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.