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A matrix $A$ is unitary if $AA^* = A^*A=I$ where $A^*=(\bar A)^T$. I would like to know, Is it true that the eigenvectors of an unitary matrix are its columns? and are these columns orthonormal?

Thanks.

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    $\begingroup$ Please do basic searching before posting questions. See here $\endgroup$ – Shailesh Dec 28 '15 at 10:39
  • $\begingroup$ @Shailesh it says: *The columns of a unitary matrix form an orthonormal set. *, ok, what about the first question? it doesn't answer that $\endgroup$ – No one Dec 28 '15 at 10:45
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The columns of an unitary matrix $A$ are othogonal, by definition. But they are not the eigenvectors of $A$, as a simple example shows: An eigenvector $\vec v$ of $A=\pmatrix{0&1\\1&0}$ is $\vec v=\pmatrix{1\\1}$.

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