A Matrix-Theoretic Perspective on Some Identities Involving Well-Known Sequences

作者：Moghaddamfar A R^*; Salehy S Navid; Salehy S Nima

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41(1): 15-28.

DOI：10.1007/s40840-015-0216-z

• Recurrence relation
• Matrix factorization
• Fibonacci sequence
• Lucas sequence
• Pell sequence
• Jacobsthal sequence

We first consider the companion matrix associated with the characteristic polynomial of a linear recurrence relation, and we investigate its powers. Next, we introduce a new matrix associated with a given linear recurrence sequence, and we get a factorization of this matrix. Finally, we give several applications of our results. Actually, we obtain some identities concerning Fibonacci, Lucas, Pell, and Jacobsthal numbers using matrix theory.

• 出版日期2018-1