The characteristic polynomial of some anti-tridiagonal 2-Hankel matrices of even order

Abstract

In this paper, we derive the characteristic polynomial for a family of anti-tridiagonal 2-Hankel matrices of even order in terms of Chebyshev polynomials, giving also a representation of its eigenvectors. An orthogonal diagonalization for these type of matrices having null northeast-to-southwest diagonal is also provided using prescribed eigenvalues.