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http://dx.doi.org/10.5831/HMJ.2020.42.2.235

ON CHARACTERIZATIONS OF SOME LINEAR COMBINATIONS INVOLVING THE MATRICES Q AND R

Ozdemir, Halim (Department of Mathematics, Sakarya University)
Karakaya, Sinan (Department of Mathematics, Sakarya University)
Petik, Tugba (Department of Mathematics, Sakarya University)

Publication Information

Honam Mathematical Journal / v.42, no.2, 2020 , pp. 235-249 More about this Journal

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 + c₂Q^m = Q^k, c₁Qⁿ + c₂Q^m = RQ^k, and c₁Qⁿ + c₂RQ^m = Q^k 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.

Keywords

Fibonacci numbers; Lucas Numbers; Matrix Equations;

Citations & Related Records

Reference

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