The Linear Algebra of the Pell-Lucas Matrix

Abstract

In this paper, we introduce the Pell-Lucas and the symmetric Pell-Lucas matrices. The study delves into the linear algebra aspects of these matrices, analyzing their mathematical properties and relationships. We construct decompositions for both the Pell-Lucas matrix and its inverse matrix. We present the Cholesky factorization of the symmetric Pell-Lucas matrices. Furthermore, we derive some valuable identities and bounds for the eigenvalues of these symmetric matrices through the application of majorization notation.

Keywords

• Pell-Lucas matrix
• symmetric Pell-Lucas matrix
• Cholesky factorization
• majorization

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