The Eigen-Problem for Some Special Near-Toeplitz Centro-Skew Tridiagonal   Matrices
  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 $R_n$. 
Antonio Behn, Kenneth R. Driessel and Irvin R. Hentzel
math.SP