Some Singular Matrices Related to -Pell and -Pell Lucas Numbers
Abstract
In this paper, we will present new singular matrices of three-by-three dimensions, whose entries of any powers of matrices are related to -Pell and -Pell Lucas numbers. Keywords : -Pell numbers ; -Pell Lucas numbers ; MatricesReferences
Catarino, P., Vasco, P. (2013) Some basic properties and a two-by-two matrix involving the k-Pell Numbers. International Journal of Mathematical Analysis, 7(45), 2209-2215.
Catarino, P., Vasco, P. (2013) On some Identities and Generating Functions for k-Pell-Lucas sequence, Applied Mathematical Sciences, 7(98), 4867- 4873.
Catarino, P. (2013). On some identities and generating functions for -Pell numbers, International Journal of Mathematical Analysis, 7(38), 1877-1884.
Cerda-Morales, G. (2019) Special Matrices Associated with Generalized Fibonacci Numbers. arXiv:1901.03736v1 [math.CO]
Horadam, A. F. (1971). Pell identities, The Fibonacci Quarterly 9(2), 245–252.
Karakaya, S., Özdemir, H., Petik, T. (2018) 3x3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers. Sakarya University Journal of Science, 22(6), 1917–1922.
Koken, F. (2020) Special Pell and Pell Lucas Matrices of Size 3x3. Düzce University Journal of Science & Technology, 8, 827-838.
Petik, T., Akbulut, H., Özdemir, H. (2021) Some 3x3 dimensional nonsingular matrices related to generalized Fibonacci numbers. Creat. Math. Inform, 30(1), 81-88.
Sergio, F., Ángel, P. (2007). On the Fibonacci k-numbers, Chaos, Solitons and Fractals, 32, 1615 – 1624.
Silvester, J. R. (1979) Fibonacci properties by matrix methods. Math. Gaz. 63(425), 188–191.
Vasco, P., Catarino, P., Campos, H., Aires, A. P., Borges, A. (2015) k -Pell, k-Pell-Lucas and Modified k-Pell Numbers: Some Identities and Norms of Hankel Matrices. International Journal of Mathematical Analysis, 9(1), 31-37.
Catarino, P., Vasco, P. (2013) On some Identities and Generating Functions for k-Pell-Lucas sequence, Applied Mathematical Sciences, 7(98), 4867- 4873.
Catarino, P. (2013). On some identities and generating functions for -Pell numbers, International Journal of Mathematical Analysis, 7(38), 1877-1884.
Cerda-Morales, G. (2019) Special Matrices Associated with Generalized Fibonacci Numbers. arXiv:1901.03736v1 [math.CO]
Horadam, A. F. (1971). Pell identities, The Fibonacci Quarterly 9(2), 245–252.
Karakaya, S., Özdemir, H., Petik, T. (2018) 3x3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers. Sakarya University Journal of Science, 22(6), 1917–1922.
Koken, F. (2020) Special Pell and Pell Lucas Matrices of Size 3x3. Düzce University Journal of Science & Technology, 8, 827-838.
Petik, T., Akbulut, H., Özdemir, H. (2021) Some 3x3 dimensional nonsingular matrices related to generalized Fibonacci numbers. Creat. Math. Inform, 30(1), 81-88.
Sergio, F., Ángel, P. (2007). On the Fibonacci k-numbers, Chaos, Solitons and Fractals, 32, 1615 – 1624.
Silvester, J. R. (1979) Fibonacci properties by matrix methods. Math. Gaz. 63(425), 188–191.
Vasco, P., Catarino, P., Campos, H., Aires, A. P., Borges, A. (2015) k -Pell, k-Pell-Lucas and Modified k-Pell Numbers: Some Identities and Norms of Hankel Matrices. International Journal of Mathematical Analysis, 9(1), 31-37.
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Published
2022-09-01
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