On characterization of being a generalized Fibonacci Q-matrix of linear combinations of two generalized Fibonacci Q-matrices

It is given a characterization of being a matrix \(Q_{g({a_3},{b_3})}^{(k)}\) of linear combination of a matrix \(Q_{g({a_1},{b_1})}^{(n)}\) and a matrix \(Q_{g({a_2},{b_2})}^{(m)}\), where \(a_{i}, b_{i} \in \mathbb {R}^{*}\), \(i=1, 2, 3\), \(m, n, k \in \mathbb {Z}\), and \(Q_{g({a},{b})}^{(l)}\) denotes an (a, b)-generalized Fibonacci Q-matrix with \(l\in \mathbb {Z}\). In addition, some examples are presented illustrating the main result. Finally, some applications of the main result obtained are given.