Asian Journal of Mathematics and Computer Research

SPECIAL MATRICES ON LUCAS AND COMPANION-LUCAS SEQUENCES

ARZU ÖZKOÇ *

Department of Mathematics, Konuralp, Faculty of Science and Art, Duzce University, Duzce, Turkey

ELIF ARDIYOK

Department of Mathematics, Konuralp, Faculty of Science and Art, Duzce University, Duzce, Turkey.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we derived some algebraic relations on circulant, negacyclic, semicirculant and companion matrices of Lucas and Companion-Lucas sequences dened by U_n = pU_n−1 − qU_n−2 and V_n = pV_n−1 − qV_n−2, with initial values U₀ = 0, U₁ = 1 and V₀ = 2, V₁ = p for n ≥ 2, where p and q are non-zero integers such that p² − 4q ≠ 0.

Keywords: Circulant matrix, lucas sequences, companion-lucas sequences, norm, determinant

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