Discussion
The eigen values of an anti-Hermitian matrix are :
Answer: C
The eigenvalues of an anti-Hermitian matrix are purely imaginary (or zero).
An anti-Hermitian matrix satisfies \( A^{\dagger} = -A \). If \( Av = \lambda v \), then
\[ \begin{aligned} v^{\dagger}Av &= \lambda\, v^{\dagger}v \\ (v^{\dagger}Av)^{*} &= v^{\dagger}A^{\dagger}v = -\lambda\, v^{\dagger}v \end{aligned} \]
so \( \lambda^{*} = -\lambda \), which means the real part of \( \lambda \) is zero. Equivalently, \( iA \) is Hermitian and has real eigenvalues.
Real eigenvalues, positive or negative, belong to Hermitian matrices, and a non-zero real part is exactly what the condition rules out.
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