Ononot — Let u = \begin{pmatrix} \frac{1}{2} \\ \frac{1}{2} \\ \frac{

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Eigenvalues & Eigenvectorshard

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Let $u = \begin{pmatrix} \frac{1}{2} \\ \frac{1}{2} \\ \frac{1}{2} \\ \frac{1}{2} \end{pmatrix}$ be a unit vector in $\mathbb{R}^4$ . Let $H = I - 2uu^T$ be the corresponding Householder matrix. What is the trace of $H^5$ ?