- #1

phrygian

- 80

- 0

## Homework Statement

Let l be an eigenvalue of an orthogonal matrix A, where l = r + is. Prove that l * conj(l) = r^2 + s^2 = 1.

## Homework Equations

## The Attempt at a Solution

I am really confused on where to go with this one.

I have Ax = A I x = A A^T A x = l^3 x

and Ax = l x so l x = l^3 x

l = l^3

l^2 = 1

l = 1 or -1

But I can't really figure out what to do from here, am I even on the right track?

Thanks for the help