Ononot — Let u = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \in \mathb

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Eigenvalues & Eigenvectorsmedium

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Let $u = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} \in \mathbb{R}^3$ . Let $A$ be the skew-symmetric matrix representing the cross product operation $Ax = u \times x$ . What are the eigenvalues of $A$ over the complex numbers $\mathbb{C}$ ?