Spectral properties for a type of heptadiagonal symmetric matrices

João Lita da Silva; João Lita da Silva

doi:10.3934/math.20231534

AIMS Mathematics

2023, Volume 8, Issue 12: 29995-30022. doi: 10.3934/math.20231534

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Spectral properties for a type of heptadiagonal symmetric matrices

João Lita da Silva ^,

Department of Mathematics and GeoBioTec, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal

Received: 09 July 2023 Revised: 21 October 2023 Accepted: 30 October 2023 Published: 06 November 2023
MSC : 15A18, 15A15, 15A09

In this paper we expressed the eigenvalues of a sort of heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From the prescribed eigenvalues, we computed eigenvectors for these types of matrices, giving also a formula not dependent on any unknown parameter for its determinant and inverse. Potential applications of the results are still provided.
- heptadiagonal matrix,
- eigenvalue,
- eigenvector,
- determinant,
- inverse matrix
Citation: João Lita da Silva. Spectral properties for a type of heptadiagonal symmetric matrices[J]. AIMS Mathematics, 2023, 8(12): 29995-30022. doi: 10.3934/math.20231534

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Abstract

In this paper we expressed the eigenvalues of a sort of heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From the prescribed eigenvalues, we computed eigenvectors for these types of matrices, giving also a formula not dependent on any unknown parameter for its determinant and inverse. Potential applications of the results are still provided.

References

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