Integer powers of real odd order skew-persymmetric anti-tridiagonal matrices with constant anti-diagonals (antitridiagn (a, c, −a), a ∈ R⧹{0}, c ∈ R)

In this paper we give the eigenvalue decomposition for real odd order skew-persymmetric anti-tridiagonal matrices with constant anti-diagonals and derive the general expression for integer powers of such matrices.