Research Article
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Year 2023, Volume: 13 Issue: 2, 170 - 186, 31.12.2023
https://doi.org/10.17678/beuscitech.1359202

Abstract

References

  • [1] M. Bayat and H. Teimoori, “The linear algebra of the generalized Pascal functional matrix”, Linear Algebra Appl., vol. 295, pp. 81-89, 1999.
  • [2] M. Bayat and H. Teimoori, “Pascal -eliminated functional matrix and its property”, Linear Algebra Appl., vol. 308 no. (1-3), pp. 65-75, 2000.
  • [3] G. S. Call and D. J. Velleman, “Pascal matrices”, Amer. Math. Monthly, vol. 100, pp. 372-376, 1993.
  • [4] M. Catalani, “Identities for Tribonacci-related sequences”, arXiv:math/0209179, https://doi.org/10.48550/arXiv.math/0209179
  • [5] E. Choi, “Modular Tribonacci numbers by matrix method”, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., vol. 20, pp. 207-221, 2013.
  • [6] S. V. Devbhadra, “Some Tribonacci identities”, Math. Today, vol. 27, pp. 1-9, 2011.
  • [7] A. Edelman and G. Strang, “Pascal matrices”, Amer. Math. Monthly, vol. 111 no. 3, pp. 189-197, 2004.
  • [8] S. Falcon, and A. Plaza, “On the Fibonacci k-numbers”, Chaos, Solitons & Fractals, vol. 32, pp. 1615-1624, 2007.
  • [9] S. Falcon, “On the k-Lucas Numbers”, International Journal of Contemporary Mathematical Sciences, vol. 6 no. 21, pp. 1039-1050, 2011.
  • [10] M. Feinberg, “Fibonacci-Tribonacci”, Fibonacci Quart., vol. 1, pp. 71-74, 1963.
  • [11] R.Frontczak, “Sums of Tribonacci and Tribonacci-Lucas Numbers”, International Journal of Mathematical Analysis, vol. 12 no. 1, pp. 19-24, 2018.
  • [12] A. F. Horadam, “Basic properties of a certain generalized sequence of numbers”, Fibonacci Quart., vol. 3, pp. 161-176, 1965.
  • [13] A. F. Horadam, “Special properties of the sequence W_n (a,b; p,q)”, Fibonacci Quart., vol. 5 no. 5, pp. 424-434, 1967.
  • [14] A. F. Horadam, “Jacobsthal representation numbers”, Fibonacci Quart., vol. 34 no. 1, 40-53, 1996.
  • [15] R. A. Horn and C. R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, Second Edition, 2013.
  • [16] F. T. Howard, “A Fibonacci Identity”, Fibonacci Quart., vol. 39, 352-357, 2001.
  • [17] D. Kalman and R. Mena, “The Fibonacci numbers-exposed”, Math. Mag., vol. 76 no. 3, 167-181, 2003.
  • [18] M. Karakas, “Some inclusion results for the new Tribonacci-Lucas matrix”, Bitlis Eren University Journal of Science and Technology, vol. 11 no. 2, 76-81, 2021.
  • [19] C. Kızılateş, N. Terzioğlu, “On r-min and r-max matrices”, Journal of Applied Mathematics and Computing, 1-30, 2022.
  • [20] E. Kilic, “Tribonacci Sequences with Certain Indices and Their Sums”, Ars Combinatoria, vol. 86, 13-22, 2008.
  • [21] E. Kilic and T. Arikan, “Studying new generalizations of Max-Min matrices with a novel approach”, Turkish Journal of Mathematics, vol. 43 no. 4, 2010-2024, 2019.
  • [22] G. Kizilaslan, “The Linear Algebra of a Generalized Tribonacci Matrix”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72 no. 1, 169-181, 2023.
  • [23] J. Li, Z. Jiang, and F. Lu, “Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers”, Abstract and Applied Analysis, vol. 4, 1-9, 2014.
  • [24] S. Pethe, “Some identities for Tribonacci sequences”, Fibonacci Quart., vol. 26, 144-151, 1988.
  • [25] T. Piezas, “A tale of four constants”, https://sites.google.com/site/tpiezas/0012
  • [26] A. Scott, T. Delaney, V. Hoggatt JR, “The Tribonacci sequence”, Fibonacci Quart., vol. 15, 193-200, 1977.
  • [27] W. Spickerman, “Binet's formula for the Tribonacci sequence”, Fibonacci Quart., vol. 20, 118-120, 1982.
  • [28] Y. Tasyurdu, “On the Sums of Tribonacci and Tribonacci-Lucas Numbers”, Applied Mathematical Sciences, vol. 13 no. 24, 1201-1208, 2019.
  • [29] R. Williamson, H. Trotter, Multivariable Mathematics, second edition, Prentice-Hall, 1979.
  • [30] C. C. Yalavigi, “Properties of Tribonacci numbers”, Fibonacci Quart., vol. 10 no. 3, 231-246, 1972.
  • [31] T. Yaying and B. Hazarika, “On sequence spaces defined by the domain of a regular tribonacci matrix”, Mathematica Slovaca, vol. 70 no. 3, 697-706, 2020.
  • [32] Z. Zhang, “The linear algebra of the generalized Pascal matrix”, Linear Algebra Appl., vol. 250, 51-60, 1997.

A Generalization of the Regular Tribonacci-Lucas Matrix

Year 2023, Volume: 13 Issue: 2, 170 - 186, 31.12.2023
https://doi.org/10.17678/beuscitech.1359202

Abstract

We define a generalization of a regular Tribonacci-Lucas matrix and give some factorizations by some special matrices. We find the inverse and the k-th power of the matrix. We also present several identities and a relation between an exponential of a matrix and the defined matrix.

References

  • [1] M. Bayat and H. Teimoori, “The linear algebra of the generalized Pascal functional matrix”, Linear Algebra Appl., vol. 295, pp. 81-89, 1999.
  • [2] M. Bayat and H. Teimoori, “Pascal -eliminated functional matrix and its property”, Linear Algebra Appl., vol. 308 no. (1-3), pp. 65-75, 2000.
  • [3] G. S. Call and D. J. Velleman, “Pascal matrices”, Amer. Math. Monthly, vol. 100, pp. 372-376, 1993.
  • [4] M. Catalani, “Identities for Tribonacci-related sequences”, arXiv:math/0209179, https://doi.org/10.48550/arXiv.math/0209179
  • [5] E. Choi, “Modular Tribonacci numbers by matrix method”, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., vol. 20, pp. 207-221, 2013.
  • [6] S. V. Devbhadra, “Some Tribonacci identities”, Math. Today, vol. 27, pp. 1-9, 2011.
  • [7] A. Edelman and G. Strang, “Pascal matrices”, Amer. Math. Monthly, vol. 111 no. 3, pp. 189-197, 2004.
  • [8] S. Falcon, and A. Plaza, “On the Fibonacci k-numbers”, Chaos, Solitons & Fractals, vol. 32, pp. 1615-1624, 2007.
  • [9] S. Falcon, “On the k-Lucas Numbers”, International Journal of Contemporary Mathematical Sciences, vol. 6 no. 21, pp. 1039-1050, 2011.
  • [10] M. Feinberg, “Fibonacci-Tribonacci”, Fibonacci Quart., vol. 1, pp. 71-74, 1963.
  • [11] R.Frontczak, “Sums of Tribonacci and Tribonacci-Lucas Numbers”, International Journal of Mathematical Analysis, vol. 12 no. 1, pp. 19-24, 2018.
  • [12] A. F. Horadam, “Basic properties of a certain generalized sequence of numbers”, Fibonacci Quart., vol. 3, pp. 161-176, 1965.
  • [13] A. F. Horadam, “Special properties of the sequence W_n (a,b; p,q)”, Fibonacci Quart., vol. 5 no. 5, pp. 424-434, 1967.
  • [14] A. F. Horadam, “Jacobsthal representation numbers”, Fibonacci Quart., vol. 34 no. 1, 40-53, 1996.
  • [15] R. A. Horn and C. R. Johnson, “Matrix Analysis”, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, Second Edition, 2013.
  • [16] F. T. Howard, “A Fibonacci Identity”, Fibonacci Quart., vol. 39, 352-357, 2001.
  • [17] D. Kalman and R. Mena, “The Fibonacci numbers-exposed”, Math. Mag., vol. 76 no. 3, 167-181, 2003.
  • [18] M. Karakas, “Some inclusion results for the new Tribonacci-Lucas matrix”, Bitlis Eren University Journal of Science and Technology, vol. 11 no. 2, 76-81, 2021.
  • [19] C. Kızılateş, N. Terzioğlu, “On r-min and r-max matrices”, Journal of Applied Mathematics and Computing, 1-30, 2022.
  • [20] E. Kilic, “Tribonacci Sequences with Certain Indices and Their Sums”, Ars Combinatoria, vol. 86, 13-22, 2008.
  • [21] E. Kilic and T. Arikan, “Studying new generalizations of Max-Min matrices with a novel approach”, Turkish Journal of Mathematics, vol. 43 no. 4, 2010-2024, 2019.
  • [22] G. Kizilaslan, “The Linear Algebra of a Generalized Tribonacci Matrix”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72 no. 1, 169-181, 2023.
  • [23] J. Li, Z. Jiang, and F. Lu, “Determinants, Norms, and the Spread of Circulant Matrices with Tribonacci and Generalized Lucas Numbers”, Abstract and Applied Analysis, vol. 4, 1-9, 2014.
  • [24] S. Pethe, “Some identities for Tribonacci sequences”, Fibonacci Quart., vol. 26, 144-151, 1988.
  • [25] T. Piezas, “A tale of four constants”, https://sites.google.com/site/tpiezas/0012
  • [26] A. Scott, T. Delaney, V. Hoggatt JR, “The Tribonacci sequence”, Fibonacci Quart., vol. 15, 193-200, 1977.
  • [27] W. Spickerman, “Binet's formula for the Tribonacci sequence”, Fibonacci Quart., vol. 20, 118-120, 1982.
  • [28] Y. Tasyurdu, “On the Sums of Tribonacci and Tribonacci-Lucas Numbers”, Applied Mathematical Sciences, vol. 13 no. 24, 1201-1208, 2019.
  • [29] R. Williamson, H. Trotter, Multivariable Mathematics, second edition, Prentice-Hall, 1979.
  • [30] C. C. Yalavigi, “Properties of Tribonacci numbers”, Fibonacci Quart., vol. 10 no. 3, 231-246, 1972.
  • [31] T. Yaying and B. Hazarika, “On sequence spaces defined by the domain of a regular tribonacci matrix”, Mathematica Slovaca, vol. 70 no. 3, 697-706, 2020.
  • [32] Z. Zhang, “The linear algebra of the generalized Pascal matrix”, Linear Algebra Appl., vol. 250, 51-60, 1997.
There are 32 citations in total.

Details

Primary Language English
Subjects Algebra and Number Theory
Journal Section Research Article
Authors

Gonca Kızılaslan 0000-0003-1816-6095

Zinnet Saral Acer 0000-0003-0990-7613

Publication Date December 31, 2023
Submission Date September 12, 2023
Published in Issue Year 2023 Volume: 13 Issue: 2

Cite

IEEE G. Kızılaslan and Z. Saral Acer, “A Generalization of the Regular Tribonacci-Lucas Matrix”, Bitlis Eren University Journal of Science and Technology, vol. 13, no. 2, pp. 170–186, 2023, doi: 10.17678/beuscitech.1359202.