Jacobsthal Matrices and their Properties

S Vasanthi; B Sivakumar

doi:10.17485/IJST/v15i5.1948

Article

Jacobsthal Matrices and their Properties

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v15i5.1948

Year: 2022, Volume: 15, Issue: 5, Pages: 207-215

Original Article

Jacobsthal Matrices and their Properties

S Vasanthi^1*, B Sivakumar²

¹Assistant Professor, Department of Mathematics, Rajalakshmi Engineering College, India
²Professor, Department of Mathematics, Rajalakshmi Engineering College, India

*Corresponding Author
Email: [email protected]

Received Date:27 November 2021, Accepted Date:05 January 2022, Published Date:13 February 2022

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: Matrices with Jacobsthal numbers are used in the medical image processing applications. The Cholesky factorization of the matrix with the Jacobsthal number is anlayzed. We also investigate the upper and lower bounds of the eigenvalues of the symmetric Jacobsthal and Jacobsthal-Lucas matrices. Methods: In this paper, we define a factor matrix and use the factorization techniques to get Cholesky decomposition of the Jacobsthal, Jacobsthal-Lucas matrix and inverses of these matrices. The bounds for eigenvalues are obtained using majorization techniques. Findings: The Cholesky factorization has been obtained using the factor matrix technique for any matrix of order n with entries from the Jacobsthal and Jacobsthal Lucas sequences. Novelty: Factorization of Lucas and symmetric Lucas matrix has already been obtained using the factorization technique. In this paper we give the factorization of the matrices with entries from the Jacobsthal and Jacobsthal Lucas sequences. Mathematics Subject Classification (2020). 15A23, 11B39, 15A18,15A42

Keywords: Jacobsthal matrix; Jacobsthal-Lucas matrix; symmetric; eigenvalues

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Copyright

© 2022 Vasanthi & Sivakumar. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published By Indian Society for Education and Environment (iSee)