Lobachevskii Journal of Mathematics

, Volume 36, Issue 1, pp 28–37 | Cite as

Explicit eigenvalues of some perturbed heptadiagonal matrices via recurrent sequences

  • S. Kouachi


In this paper we present a direct method to calculate explicit expressions of eigenvalues of some perturbed heptadiagonal matrices. The method is of interest to engineers and statisticians since it is based on elementary properties of determinants and recurrent sequences. The use and even the knowledge of the theory of orthogonal polynomials, which was usually necessary (see for example [2]) is not needed here. Once the needed recurent relations are obtained, we use the theory of recurrent sequences and trigonometric formulas.

Keywords and phrases

Eigenvalues heptadiagonal matrices characteristic polynomial recurrent relation 


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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceQassim UniversityAl-Gassim, BuraydahSaudi Arabia

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