Let be an imaginary eigenvalue of an orthogonal matrix Q adn let X be a corresponding eigenvector. Prove that

Ok here is what I did:

Also

So

i.e.

i.e. or

Why can't ?

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- Mar 13th 2009, 07:11 AMslevvioOrthogonal Matrix
Let be an imaginary eigenvalue of an orthogonal matrix Q adn let X be a corresponding eigenvector. Prove that

Ok here is what I did:

Also

So

i.e.

i.e. or

Why can't ? - Mar 13th 2009, 07:17 AMInvisibleMan
Hi, it should be alpha^2 and not |alpha|^2 cause you don't take complex conjugate but rather the transpose only, and because alpha=ai a is real, alpha^2=-a^2 so it cannot be equal 1.