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SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3

Year 2020, , 827 - 838, 31.01.2020
https://doi.org/10.29130/dubited.582108

Abstract

In
this study, we study on special Pell and Pell Lucas matrices of order 3x3, entries of whose nth powers are related specific Pell and Pell Lucas
numbers with indices certain positive integer according to powers these
matrices.

References

  • [1] B. D. Bitim, “Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices”, Düzce University Journal of Science & Technology, vol.7, no.1, pp.606–615, 2019.
  • [2] J. Ercolano, “Matrix generator of Pell sequence”, The Fibonacci Quarterly, vol.17, no.1, pp. 71–77, 1979.
  • [3] R.S. Melham, “Lucas Sequences and Functions of a 3-by-3 Matrix”, The Fibonacci Quarterly, 37.2, 111–116, 1999.
  • [4] A. F. Horadam, “Pell identities”, The Fibonacci Quarterly, vol.9, no.3, pp. 245–252, 263, 1971.
  • [5] S. Karakaya, H. Özdemir, T. Petik, “3×3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers”, Sakarya University Journal of Science, vol.22, no.6, 1917–1922, 2018.
  • [6] F. Koken ve S. Arslan, “Pell ve Pell Lucas sayılarının Özellikleri”, XXIII. Ulusal Matematik Sempozyumu, Kayseri,Türkiye, ss:85, 2010.
  • [7] F. Koken, “The Representations of the Pell and Pell Lucas Matrices”, International Marmara Science And Social Sciences Congress, Kocaeli, Türkiye, Proceedings Book I (Science), ss: 466–473, 2019.
  • [8] T. Koshy, Pell and Pell-Lucas numbers with application, Springer New York Heidelberg Dordrecht London, pp. 115–172, 2014.

Special Pell And Pell Lucas Matrices Of Size 3x3

Year 2020, , 827 - 838, 31.01.2020
https://doi.org/10.29130/dubited.582108

Abstract

Bu çalışmada, 3x3 boyutlu matrisler için, matrisin n. kuvvetinin elemanları bu matrislerin
kuvvetlerine göre belirli pozitif tamsayı indisli Pell ve Pell Lucas sayıları
ile ilişkilendirilerek, özel Pell ve Pell Lucas matrisleri üzerinde çalışıldı.

References

  • [1] B. D. Bitim, “Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices”, Düzce University Journal of Science & Technology, vol.7, no.1, pp.606–615, 2019.
  • [2] J. Ercolano, “Matrix generator of Pell sequence”, The Fibonacci Quarterly, vol.17, no.1, pp. 71–77, 1979.
  • [3] R.S. Melham, “Lucas Sequences and Functions of a 3-by-3 Matrix”, The Fibonacci Quarterly, 37.2, 111–116, 1999.
  • [4] A. F. Horadam, “Pell identities”, The Fibonacci Quarterly, vol.9, no.3, pp. 245–252, 263, 1971.
  • [5] S. Karakaya, H. Özdemir, T. Petik, “3×3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers”, Sakarya University Journal of Science, vol.22, no.6, 1917–1922, 2018.
  • [6] F. Koken ve S. Arslan, “Pell ve Pell Lucas sayılarının Özellikleri”, XXIII. Ulusal Matematik Sempozyumu, Kayseri,Türkiye, ss:85, 2010.
  • [7] F. Koken, “The Representations of the Pell and Pell Lucas Matrices”, International Marmara Science And Social Sciences Congress, Kocaeli, Türkiye, Proceedings Book I (Science), ss: 466–473, 2019.
  • [8] T. Koshy, Pell and Pell-Lucas numbers with application, Springer New York Heidelberg Dordrecht London, pp. 115–172, 2014.
There are 8 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fikri Köken 0000-0002-8304-9525

Publication Date January 31, 2020
Published in Issue Year 2020

Cite

APA Köken, F. (2020). SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3. Duzce University Journal of Science and Technology, 8(1), 827-838. https://doi.org/10.29130/dubited.582108
AMA Köken F. SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3. DÜBİTED. January 2020;8(1):827-838. doi:10.29130/dubited.582108
Chicago Köken, Fikri. “SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3”. Duzce University Journal of Science and Technology 8, no. 1 (January 2020): 827-38. https://doi.org/10.29130/dubited.582108.
EndNote Köken F (January 1, 2020) SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3. Duzce University Journal of Science and Technology 8 1 827–838.
IEEE F. Köken, “SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3”, DÜBİTED, vol. 8, no. 1, pp. 827–838, 2020, doi: 10.29130/dubited.582108.
ISNAD Köken, Fikri. “SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3”. Duzce University Journal of Science and Technology 8/1 (January 2020), 827-838. https://doi.org/10.29130/dubited.582108.
JAMA Köken F. SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3. DÜBİTED. 2020;8:827–838.
MLA Köken, Fikri. “SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3”. Duzce University Journal of Science and Technology, vol. 8, no. 1, 2020, pp. 827-38, doi:10.29130/dubited.582108.
Vancouver Köken F. SPECIAL PELL AND PELL LUCAS MATRICES OF ORDER 3X3. DÜBİTED. 2020;8(1):827-38.