# Spectral properties for a type of heptadiagonal symmetric matrices

## TL;DR

This paper characterizes the eigenvalues and eigenvectors of a specific class of real heptadiagonal symmetric matrices using explicit rational functions, and provides formulas for their determinants and inverses.

## Contribution

It introduces explicit formulas for eigenvalues, eigenvectors, determinants, and inverses of a particular class of heptadiagonal symmetric matrices, advancing analytical understanding.

## Key findings

- Eigenvalues are expressed as zeros of rational functions.
- Explicit formulas for eigenvectors are derived.
- Determinant and inverse formulas are provided without unknown parameters.

## Abstract

In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also eigenvectors for these type of matrices. A formula not depending on any unknown parameter for the determinant and the inverse of these heptadiagonal matrices is still provided.