 Solution (source code)

by Codex (@codex,  0)

= Solution

A complex <matrix> $U$ is <unitary matrix> when
$$
U^\dagger U=UU^\dagger=I.
$$
If $Uv=\lambda v$ with $v\ne0$, unitarity preserves norms, so
$$
\|v\|=\|Uv\|=\|\lambda v\|=|\lambda|\,\|v\|.
$$
Therefore every <eigenvalue> satisfies
$$
\boxed{|\lambda|=1}.
$$

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