Spectral properties for a type of heptadiagonal symmetric matrices

João Lita da Silva

doi:10.3934/math.20231534

Spectral properties for a type of heptadiagonal symmetric matrices

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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.

Original language	English
Pages (from-to)	29995-30022
Number of pages	28
Journal	AIMS Mathematics
Volume	8
Issue number	12
DOIs	https://doi.org/10.3934/math.20231534
Publication status	Published - 6 Nov 2023

Keywords

determinant
eigenvalue
eigenvector
heptadiagonal matrix
inverse matrix

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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.",

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KW - inverse matrix

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Spectral properties for a type of heptadiagonal symmetric matrices

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Keywords

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