Orthogonal matrices by definition have real entries. The complex analogue is called "unitary".
Hi all, just wanted to make sure I have this right -
My lecture notes say that the eigenvalues of orthogonal matrices have magnitude 1. When I looked through the proof it seemed to me like the statement should have said *real* orthogonal matrices.
So I played around a little bit and I think I came up with a counterexample to show the eigenvalues of any orthogonal matrix don't have magnitude 1:
(LaTeX isn't co-operating, sorry)
Q = [2i, sqrt{5} ; sqrt{5}, -2i]
is orthogonal but has eigenvalues 2i & -1/(2i), which don't have magnitude 1...
All good? Anything I missed?
Thanks a lot