# 2018-07 A tridiagonal matrix

Let $$S$$ be an $$(n+1) \times (n+1)$$ matrix defined by
$S_{ij} = \begin{cases} (n+1)-i & \text{ if } j=i+1, \\ i-1 & \text{ if } j=i-1, \\ 0 & \text{ otherwise. } \end{cases}$
Find all eigenvalues of $$S$$.

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