Jacobsthal Matrices and their Properties

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.