Re: Diagonalization of an orthogonal matrix with determinant 1
- From: "Lucillon" <nospam@xxxxxx>
- Date: Wed, 24 Oct 2007 16:59:04 +0200
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. Use the Spectral
Theorem.
How do you see that orthogonal matrices are unitary? I agree for the real
matrices but how about the complex matri ces?
.
- References:
- Diagonalization of an orthogonal matrix with determinant 1
- From: Lucillon
- Re: Diagonalization of an orthogonal matrix with determinant 1
- From: Robert Israel
- Diagonalization of an orthogonal matrix with determinant 1
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