Homework for Periodic Systems

  1. (AntiHermitian)

    Show that the eigenvalues of anti-Hermitian matrices are pure imaginary.

  2. (MatrixExponentials)

    Given the following matrix \begin{align} A &= \frac{1}{\sqrt{3}} \left[ \begin{array}{rrr} 0 & -i & i \\ i & 0 & -i \\ -i & i & 0 \end{array} \right] \end{align}

    1. Find $e^{iA\theta}$.

    2. Evaluate $e^{iA\theta}$ at $\theta=\frac{2\pi}{3}$.


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