Ononot — Let u = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} be a unit

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Eigenvalues & Eigenvectorshard

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Let $u = \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}$ be a unit vector in $\mathbb{R}^3$ . Define the linear operator $T: \mathbb{R}^3 \to \mathbb{R}^3$ by $T(x) = u \times x$ . What are the eigenvalues of the matrix representation of $T$ ?