(adsbygoogle = window.adsbygoogle || []).push({}); Q: Prove htat if a matrix U is unitary, then all eigenvalues of U have absolute value 1.

My try:

Suppose U*=U^-1 (or U*U=I)

Let UX=(lambda)X, X nonzero

=> U*UX=(lambda) U*X

=> X=(lambda) U*X

=> ||X||=|lambda| ||U*X||

=> |lambda| = ||X|| / ||(U^-1)X||

And now I am really stuck and hopeless, what can I do?

Thanks for helping!

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# Homework Help: Eigenvalues of a unitary matrix

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