On the generating matrices of thee Κ-Fibonacci numbers


  • Sergio Falcon Universidad de las Palmas.




k-Fibonacci numbers, Cofactor matrix, Eigenvalues.


In this paper we define some tridiagonal matrices depending of a parameter from which we will find the k-Fibonacci numbers. And from the cofactor matrix of one of these matrices we will prove some formulas for the k-Fibonacci numbers differently to the traditional form. Finally, we will study the eigenvalues of these tridiagonal matrices.

Author Biography

Sergio Falcon, Universidad de las Palmas.

Department of Mathematics 35017-Las Palmas de Gran Canaria.


[1] Falcon S. and Plaza A., On the Fibonacci k-numbers, Chaos, Solit. & Fract. 32 (5), pp. 1615—1624, (2007).

[2] Falcon S. and Plaza A., The k-Fibonacci sequence and the Pascal 2-triangle, Chaos, Solit. & Fract. 33 (1), pp. 38—49, (2007).

[3] Falcon S. and Plaza A., The k-Fibonacci hyperbolic functions, Chaos, Solit. & Fract. 38 (2), pp. 409—420, (2008).

[4] Feng A., Fibonacci identities via determinant of tridiagonal matrix, Applied Mathematics and Computation, 217, pp. 5978—5981, (2011).

[5] Horn R. A. and Johnson C. R., Matrix Analysis, p. 506, Cambridge University Press (1991).

[6] Hoggat V. E. Fibonacci and Lucas numbers, Houghton—Miffin, (1969).

[7] Horadam A. F. A generalized Fibonacci sequence, Mathematics Magazine, 68, pp. 455—459, (1961).

[8] Usmani R., Inversion of a tridiagonal Jacobi matrix, Linear Algebra Appl. 212/213, pp. 413—414, (1994). [9] Wikipedia, http://en.wikipedia.org/wiki/Cofactor matrix

How to Cite

S. Falcon, “On the generating matrices of thee Κ-Fibonacci numbers”, Proyecciones (Antofagasta, On line), vol. 32, no. 4, pp. 347-357, 1.