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Spectral properties of anti-heptadiagonal persymmetric Hankel matrices

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Abstract

In this paper we express the eigenvalues of anti-heptadiagonal persymmetric Hankel matrices as the zeros of explicit polynomials giving also a representation of its eigenvectors. We present also an expression depending on localizable parameters to compute its integer powers. In particular, an explicit formula not depending on any unknown parameter for the inverse of anti-heptadiagonal persymmetric Hankel matrices is provided.

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Acknowledgements

This work is a contribution to the Project UIDB/04035/2020, funded by FCT-Fundação para a Ciência e a Tecnologia, Portugal.

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Correspondence to João Lita da Silva.

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Communicated by Fuzhen Zhang.

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Lita da Silva, J. Spectral properties of anti-heptadiagonal persymmetric Hankel matrices. Banach J. Math. Anal. 14, 1387–1420 (2020). https://doi.org/10.1007/s43037-020-00066-x

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  • DOI: https://doi.org/10.1007/s43037-020-00066-x

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