Research Article
Bicomplex Numbers: Further Contributions to a Fibonacci and Fibonacci -Lucas Matrices Oriented Approach
Abstract
In this study, by using Fibonacci Q-matrix and Lucas Q^'-matrix we define bicomplex Fibonacci Q-matrix and bicomplex Lucas Q^'-matrix. After that using this matrix representation, we give some identities.
References
- Referans1 Price G. B. 1991. An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, Inc: New York. I(1)-44(1).
- Referans2 Dunlap R. A. 1997. The Golden Ratio and Fibonacci Numbers. World Scientific Press.
- Referans3 Vajda S. 1989. Fibonacci and Lucas numbers, and the Golden Section. Theory and Applications, Halsted Press.
- Referans4 Hoggatt V. E. 1969. Fibonacci and Lucas Numbers published by The Fibonacci Association.
- Referans5 Iyer M. R. 1969. Some Results on Fibonacci Quaternions. The Fibonacci Quarterly, 7(2), 201-210.
- Referans6 Knuth D. 2013. Negafibonacci Numbers and Hyperbolic Plane. Annual Meeting of the Math. Association of America.
- Referans7 Horadam A. F. 191. A Generalized Fibonacci Sequence. American Math. Monthly, 68.
- Referans8 Iyer M. R. 1969. Identities Involving Generalized Fibonacci Numbers. the Fibonacci Quarterly, 7(1), 66-72.
- Referans9 Lucas E. 1961. Théorie des Numbers, 1(520). 25 Nf. Balanchard, Paris.
- Referans10 Koshy T. 2001. Fibonacci and Lucas Numbers with Applications. Wiley-Intersience Publication, New York.
- Referans11 Basin S. L. Hoggatt V. E. 1963. A Primer on the Fibonacci Sequence, Part II. Fib. Quart. 1, 61-68.
- Referans12 Brenner J. L. 1951. June Meeting of the Pacific Northwest Section. 1. Lucas Matrix. Amer. Math. Monthly , 58, 220-221.
- Referans13 Honsberger R. 1985. The Matrix Q. Mathematical Gems III. Washington, DC: Math. Assoc. Amer. 106-107.
- Referans14 King C. H. 1960. Some Further Properties of the Fibonacci Numbers. Master's thesis. San Jose, CA: San Jose State.
- Referans15 Köken F. and Bozkurt D. 2010. On lucas numbers by the matrix method Hacettepe Journal of Mathematics and Statistics 39(4), 471-475.
- Referans16 Glynn D. G. 2010. Permanenet of a square matrix. European Journal of Combinatorics, 31(7), 1891-1897.
Year 2021,
Volume: 10 Issue: 4, 1386 - 1393, 31.12.2021
Abstract
Bu çalışmada, Fibonacci Q -matrisi kullanılarak bikompleks Fibonacci Q -matris and bikompleks Lucas Q -matrisi tanımladık. Daha sonra bu matris sunumunu kullanarak bazı özdeşlikler verdik.
In this study, by using Fibonacci Q -matrix we define bicomplex Fibonacci Q -matrix and bicomplex Lucas Q^' -matrix. After that using this matrix representation, we give some identities.
References
- Referans1 Price G. B. 1991. An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, Inc: New York. I(1)-44(1).
- Referans2 Dunlap R. A. 1997. The Golden Ratio and Fibonacci Numbers. World Scientific Press.
- Referans3 Vajda S. 1989. Fibonacci and Lucas numbers, and the Golden Section. Theory and Applications, Halsted Press.
- Referans4 Hoggatt V. E. 1969. Fibonacci and Lucas Numbers published by The Fibonacci Association.
- Referans5 Iyer M. R. 1969. Some Results on Fibonacci Quaternions. The Fibonacci Quarterly, 7(2), 201-210.
- Referans6 Knuth D. 2013. Negafibonacci Numbers and Hyperbolic Plane. Annual Meeting of the Math. Association of America.
- Referans7 Horadam A. F. 191. A Generalized Fibonacci Sequence. American Math. Monthly, 68.
- Referans8 Iyer M. R. 1969. Identities Involving Generalized Fibonacci Numbers. the Fibonacci Quarterly, 7(1), 66-72.
- Referans9 Lucas E. 1961. Théorie des Numbers, 1(520). 25 Nf. Balanchard, Paris.
- Referans10 Koshy T. 2001. Fibonacci and Lucas Numbers with Applications. Wiley-Intersience Publication, New York.
- Referans11 Basin S. L. Hoggatt V. E. 1963. A Primer on the Fibonacci Sequence, Part II. Fib. Quart. 1, 61-68.
- Referans12 Brenner J. L. 1951. June Meeting of the Pacific Northwest Section. 1. Lucas Matrix. Amer. Math. Monthly , 58, 220-221.
- Referans13 Honsberger R. 1985. The Matrix Q. Mathematical Gems III. Washington, DC: Math. Assoc. Amer. 106-107.
- Referans14 King C. H. 1960. Some Further Properties of the Fibonacci Numbers. Master's thesis. San Jose, CA: San Jose State.
- Referans15 Köken F. and Bozkurt D. 2010. On lucas numbers by the matrix method Hacettepe Journal of Mathematics and Statistics 39(4), 471-475.
- Referans16 Glynn D. G. 2010. Permanenet of a square matrix. European Journal of Combinatorics, 31(7), 1891-1897.
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Araştırma Makalesi |
| Authors | |
| Publication Date | December 31, 2021 |
| Submission Date | June 18, 2021 |
| Acceptance Date | October 19, 2021 |
| Published in Issue | Year 2021 Volume: 10 Issue: 4 |
Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS
E-mail: fbe@beu.edu.tr