On determinants of matrices with general Fibonacci numbers entries

@article{Karaduman2005OnDO,
  title={On determinants of matrices with general Fibonacci numbers entries},
  author={Erdal Karaduman},
  journal={Appl. Math. Comput.},
  year={2005},
  volume={167},
  pages={670-676}
}
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References

SHOWING 1-3 OF 3 REFERENCES
An application of Fibonacci numbers in matrices
Generalized Fibonacci numbers by matrix methods
TLDR
Difference equations of the form (2) are expressible in a matrix form analogous to (1) and may be viewed as the solution to n+2 ~ n + n+l which has initial terms uQ = 0 and u1 = 1.
Sums of Fibonacci numbers by matrix methods, The Fibonacci Quarterly
  • 1984