Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON CHARACTERIZATIONS OF SOME LINEAR COMBINATIONS INVOLVING THE MATRICES Q AND R

  • Received : 2019.02.21
  • Accepted : 2020.03.16
  • Published : 2020.06.25
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Abstract

Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c1Qn + c2Qm = Qk, c1Qn + c2Qm = RQk, and c1Qn + c2RQm = Qk with unknowns c1, c2 ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.

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Acknowledgement

The authors are very thankful to two anonymous referees who made a very careful reading and many valuable comments, corrections and suggestions.

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