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The characteristic polynomial of some anti-tridiagonal 2-Hankel matrices of even order
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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.
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Anti-tridiagonal 2-Hankel matrix Chebyshev polynomials Eigenvalue Eigenvector General