Solution
= Solution
Let $Av=\lambda v$ with $v\ne0$. Taking the <Hermitian inner product> with $v$ gives $v^\dagger Av=\lambda\|v\|^2$. For an <anti-Hermitian matrix>,
$$
\overline{v^\dagger Av}=v^\dagger A^\dagger v=-v^\dagger Av.
$$
Consequently $\overline\lambda\|v\|^2=-\lambda\|v\|^2$. As $\|v\|^2>0$, the <eigenvalue> satisfies $\boxed{\overline\lambda=-\lambda}$, or $\boxed{\lambda=i\theta\text{ with }\theta\in\mathbb R}$. Zero is included as a purely imaginary <eigenvalue>.