Some 3×3 dimensional nonsingular matrices related to generalized Fibonacci numbers

 Petik, Tuğba, Akbulut, Hilal and  Özdemir, Halim

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The relation between integer powers of the generalized Fibonacci matrix
{Q_g} = \left( {\begin{array}{*{20}{c}} p&q\\ 1&0 \end{array}} \right) and generalized Fibonacci numbers is well known, where p and q are nonzero real numbers. Inspired by this relation, a procedure is presented to find some 3 \times 3 dimensional nonsingular matrices whose powers are related to generalized Fibonacci numbers.

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 Petik, Tuğba, Akbulut, Hilal, Özdemir, Halim