# Thread: Eigenvalues of orthogonal matrices

1. ## Eigenvalues of orthogonal matrices

How does one prove the eigenvalues of an orthogonal matrix lie on the unit circle?

2. Originally Posted by kiwijoey
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:

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

Tonio