I have been learning basic types of matrices, when I came across the following problem: Prove that the eigenvalues of orthogonal matrices are of unit modulus. And the solution mentioned that since Orthogonal matrices are unitary matrices, so the result held good as the same result had already been proven in case of Unitary Matrices. I had the following questions in my mind next:
- Are all elements of an orthogonal matrix real? Why can't they be complex?
- Can a complex matrix be orthogonal?
Any productive discussion is looked forward to. And I think what might better help the discussion is an example of a "COMPLEX ORTHOGONAL MATRIX".