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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, K. N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran

    A. R. Moghaddamfar

  2. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    S. Navid Salehy & S. Nima Salehy

Authors
  1. A. R. Moghaddamfar
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  2. S. Navid Salehy
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  3. S. Nima Salehy
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Corresponding author

Correspondence to A. R. Moghaddamfar.

Additional information

Communicated by Emrah Kilic.

In memory of Professor Michael Neumann.

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Moghaddamfar, A.R., Salehy, S.N. & Salehy, S.N. A Matrix-Theoretic Perspective on Some Identities Involving Well-Known Sequences. Bull. Malays. Math. Sci. Soc. 41, 15–28 (2018). https://doi.org/10.1007/s40840-015-0216-z

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  • DOI: https://doi.org/10.1007/s40840-015-0216-z

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