On Characterization of Being a Matrix Q (k) g(a2,b2) of Linear Combinations of a Matrix Q (n) g(a1,b1) and a Matrix Q m

Authors : Aslı ÖNDÜL, Halim ÖZDEMİR, Tuğba PETİK

Pages : 361-364

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Publication Date : 2020-10-27

Article Type : Research Paper

Abstract :It is given a characterization of all solution of the matrix equation $c_{1}Q_{ginsert ignore into journalissuearticles values(a_{1}, b_{1});}^{insert ignore into journalissuearticles values(n);}+c_{2}Q^{m}=Q_{ginsert ignore into journalissuearticles values(a_{2}, b_{2});}^{insert ignore into journalissuearticles values(k);}$ with unknowns $c_{1}, c_{2} \in \mathbb{C}^{*}$. Here the matrix $Q_{ginsert ignore into journalissuearticles values(a, b);}^{insert ignore into journalissuearticles values(l);}$, called an $l$-generalized Fibonacci $Q$-matrix, is defined by means of the Fibonacci $Q$-matrix, where $l$ is an integer, and $a, b \in \mathbb{R}^{*}$.                      
Keywords : Fibonacci Numbers, Fibonacci Q matrix, Generalized Fibonacci Numbers, Linear Combination, Matrix Equations