Re: Diagonalization of an orthogonal matrix with determinant 1

In article <rbisrael.20071024032433$6914@xxxxxxxxxxxxxxxx>, Robert
Israel <israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

"Lucillon" <nospam@xxxxxx> writes:

I have just seen that every matrix in the special orthogonal group
SO(n,Complexnumbers)={A in M(n,C) where
Transpose(A)A=ATranspose(A)=identity-matrix and det(A)= 1}, can be
diagonalized using Lie-group theory. Does any body know how to show this
in
a simpler way for example using linear algebra?

Orthogonal matrices are unitary, and thus normal.

These are complex orthogonal matrices: we use the transpose in
the definition, not the conjugate transpose. So is it clear they
are unitary?

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.