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Math Help - Eigenvalues of orthogonal matrices

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    Eigenvalues of orthogonal matrices

    How does one prove the eigenvalues of an orthogonal matrix lie on the unit circle?
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    Quote Originally Posted by kiwijoey View Post
    How does one prove the eigenvalues of an orthogonal matrix lie on the unit circle?

    If x is an eigenvector of an orthogonal matrix U with corresponding eigenvalue[/tex]\lambda[/tex] , then:

    \|x\|=\|Ux\|=\|\lambda x\|=|\lambda|\|x\|

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