Spectral properties for a type of heptadiagonal symmetric matrices

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.

Keywords

• heptadiagonal matrix
• eigenvalue
• eigenvector
• determinant
• inverse matrix