Diagonalize $$$\left[\begin{array}{cccc}\frac{1}{2} & \frac{1}{2} & 0 & 0\\\frac{1}{2} & 0 & \frac{1}{2} & 0\\\frac{1}{2} & 0 & 0 & \frac{1}{2}\\0 & 0 & 0 & 1\end{array}\right]$$$
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Diagonalize $$$\left[\begin{array}{cccc}\frac{1}{2} & \frac{1}{2} & 0 & 0\\\frac{1}{2} & 0 & \frac{1}{2} & 0\\\frac{1}{2} & 0 & 0 & \frac{1}{2}\\0 & 0 & 0 & 1\end{array}\right]$$$.
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