On Some Matrix Representations of Bicomplex Numbers

Abstract

In this work, we have defined bicomplex numbers whose coefficients are from the Fibonacci sequence. We examined the matrix representations and algebraic properties of these numbers. We also computed the eigenvalues and eigenvectors of these particular matrices.

Keywords

• Bicomplex numbers,Recurrences

References

1. [1] Elizarraras, L. Bicomplex numbers and their elementary functions. Cubo, Temuco. 14, 2 (2012), 61–80.
2. [2] Elizarraras, L. Bicomplex holomorphic functions : The algebra, geometry and analysis of bicomplex numbers, vol. 2015. 2015.
3. [3] Halıcı, S. On fibonacci quaternions. Advances in Applied Clifford Algebras 22, 2 (2012), 321–327.
4. [4] Halıcı, S. On bicomplex fibonacci numbers and theirs generalization. In Models and Theories in Social Systems (2019).
5. [5] Horadam, A. F. Complex fibonacci numbers and fibonacci quaternions. The American Mathematical Monthly 70, 3 (1963), 289–291.
6. [6] Horadam, A. F. Basic properties of a certain generalized sequence of numbers. Fibonacci Quart. 3, 3 (1965), 161–176.
7. [7] Koshy, T. Fibonacci and Lucas numbers with applications. 2011.
8. [8] Torunbalcı, A. Bicomplexfibonacci quaternions. Chaos, Solitons and Fractals 106 (2018), 147–153.