The eigenvalues of some anti-tridiagonal Hankel matrices

Abstract

We determine the spectra of two families of anti-tridiagonal Hankel matrices of any order. The approach is much stronger and more concise than those particular cases appearing in the literature. At the same time, it simplifies significantly all the known results up to now.

Keywords

• Anti-tridiagonal matrices
• Hankel matrices
• Chebyshev polynomials
• eigenvalues