Powers of real persymmetric anti-tridiagonal matrices with constant anti-diagonals

摘要

In this paper, we present an eigenvalue decomposition with an orthogonal eigenvector matrix for any real persymmetric anti-tridiagonal matrix with constant anti-diagonals. Furthermore, we derive a general expression for the entries of the powers of these anti-tridiagonal matrices in terms of the Chebyshev polynomials of the second kind.