  Let $n\ge 2$ be an integer. Let $R_n$ denote the $n\times n$ tridiagonal
matrix with $-1$'s on the sub-diagonal, $1$'s on the super-diagonal, $-1$ in
the $(1,1)$ entry, $1$ in the $(n,n)$ entry and zeros elsewhere. We find the
eigen-pairs of the matrices $R_n$.
