The Pell and Pell-Lucas Numbers via Square Roots of Matrices

Authors

  • Saadet Arslan Department of Mathematics, Ahmet Kelesoglu Faculty of Education, Necmettin Erbakan University, Konya
  • Fikri Köken Konya Ereğli Kemal Akman Vocational School, Necmettin Erbakan University, Konya

DOI:

https://doi.org/10.26713/jims.v8i3.393

Keywords:

Pell and Pell-Lucas Numbers, Square Roots of Matrices

Abstract

In this paper, the Pell and Pell-Lucas numbers with specialized rational subscripts are derived from general expressions by square roots of the matrices Mn and Nn. Besides, we reveal that the identities involving these numbers are produced by square roots of matrices Mn/2 and Nn/2. Further we show that the matrices Mn and Nn are generalized to rational powers by using the Abel's functional equation.

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References

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(1971), 245-252; 263.

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D. Sullivan, The square roots of (2 times 2) matrices, Math. Magazine 66 (5) (1993).

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Published

2016-11-09
CITATION

How to Cite

Arslan, S., & Köken, F. (2016). The Pell and Pell-Lucas Numbers via Square Roots of Matrices. Journal of Informatics and Mathematical Sciences, 8(3), 159–166. https://doi.org/10.26713/jims.v8i3.393

Issue

Vol. 8 No. 3 (2016)

Section

Research Article

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