Finding Eigenvectors for a Real Canonical Form of Matrix A

[ItsKP]

Homework Statement

Let A= [0 2 1;-2 3 0;1 0 2]
Determine a real canonical form of A and give a change of basis matrix P that brings the matrix into this form.

Homework Equations

The Attempt at a Solution

I found my eigenvalues to be 0, 2+i and 2-i.
So, taking 2+i, I get the real canonical form
[0 0 0; 0 2 1; 0 -1 2].
Now using 2+i how do I find the eigenvalues to find a P that contains the 3 eigenvectors?

 

[lanedance]

i think your eigenvalues should be
1, 2+i and 2-i