Research Article
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Year 2023, Volume: 72 Issue: 1, 169 - 181, 30.03.2023

Gonca Kızılaslan

https://doi.org/10.31801/cfsuasmas.1052686
Cited By: 1

Abstract

References

  • Bayat, M., Teimoori, H., The linear algebra of the generalized Pascal functional matrix, Linear Algebra Appl., 295 (1999), 81–89. https://dx.doi.org/10.1016/S0024-3795(99)00062-2
  • Bayat, M., Teimoori, H., Pascal k−eliminated functional matrix and its property, Linear Algebra Appl., 308 (1–3) (2000), 65–75. https://dx.doi.org/10.1016/S0024-3795(99)00266-9
  • Call, G. S., Velleman, D. J., Pascal matrices, Amer. Math. Monthly, 100 (1993), 372–376. https://doi.org/10.1080/00029890.1993.11990415
  • Catalani, M., Identities for Tribonacci-related sequences, arXiv:math/0209179 [math.CO]. https://doi.org/10.48550/arXiv.math/0209179
  • Choi, E., Modular Tribonacci numbers by matrix method, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 20 (2013), 207–221. https://dx.doi.org/10.7468/jksmeb.2013.20.3.207
  • Devbhadra, S. V., Some Tribonacci identities, Math. Today, 27 (2011), 1–9.
  • Edelman, A., Strang, G., Pascal matrices, Amer. Math. Monthly, 111 (3) (2004), 189–197. https://dx.doi.org/10.1080/00029890.2004.11920065
  • Falcon, S., Plaza, A., On the Fibonacci k−numbers, Chaos, Solitons & Fractals, 32 (2007), 1615–1624. https://dx.doi.org/10.1016/j.chaos.2006.09.022
  • Falcon, S., On the k−Lucas Numbers, International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039–1050.
  • Feinberg, M., Fibonacci-Tribonacci, Fibonacci Quart., 1 (1963), 71–74.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3 (1965), 161–176.
  • Horadam, A. F., Special properties of the sequence $W_n(a, b; p, q)$, Fibonacci Quart., 5 (5) (1967), 424–434.
  • Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quart., 34 (1) (1996), 40–53.
  • Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, Second Edition, 2013.
  • Howard, F. T., A Tribonacci identity, Fibonacci Quart., 39 (2001), 352–357.
  • Jakubczyk, Z., Sums of Squares of Tribonacci Numbers, Advanced problems and solutions edited by Florian Luca, The Fibonacci Quarterly, August (2013), 4–5.
  • Kalman, D., Mena, R., The Fibonacci numbers-exposed, Math. Mag., 76 (3) (2003), 167–181. https://dx.doi.org/10.1080/0025570X.2003.11953176
  • Kızılateş, C., Terzioğlu, N., On r−min and r−max matrices, Journal of Applied Mathematics and Computing, (2022), 1–30. https://dx.doi.org/10.1007/s12190-022-01717-y
  • Kilic, E., Arikan, T., Studying new generalizations of Max-Min matrices with a novel approach, Turkish Journal of Mathematics, 43 (4) (2019), 2010–2024.
  • Pethe, S., Some identities for Tribonacci sequences, Fibonacci Quart., 26 (1988), 144–151.
  • Piezas, T., A tale of four constants, https://sites.google.com/site/tpiezas/0012.
  • Scott, A., Delaney, T., Hoggatt J. R., V., The Tribonacci sequence, Fibonacci Quart., 15 (1977), 193–200.
  • Spickerman, W., Binet’s formula for the Tribonacci sequence, Fibonacci Quart., 20 (1982), 118–120.
  • Williamson, R., Trotter, H., Multivariable Mathematics, second edition, Prentice-Hall, 1979.
  • Yalavigi, C. C., Properties of Tribonacci numbers, Fibonacci Quart., 10 (3) (1972), 231–246.
  • Yaying, T., Hazarika, B., On sequence spaces defined by the domain of a regular Tribonacci matrix, Mathematica Slovaca, 70 (3) (2020), 697–706. https://dx.doi.org/10.1515/ms-2017-0383
  • Zhang, Z., The linear algebra of the generalized Pascal matrix, Linear Algebra Appl., 250 (1997), 51–60. https://dx.doi.org/10.1016/0024-3795(95)00452-1

The linear algebra of a generalized Tribonacci matrix

Year 2023, Volume: 72 Issue: 1, 169 - 181, 30.03.2023

Gonca Kızılaslan

https://doi.org/10.31801/cfsuasmas.1052686
Cited By: 1

Abstract

In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k−th power. We also give a relation between the matrix and a matrix exponential of a special matrix.

Keywords

Tribonacci sequence factorization of matrices matrix exponential matrix inverse

References

  • Bayat, M., Teimoori, H., The linear algebra of the generalized Pascal functional matrix, Linear Algebra Appl., 295 (1999), 81–89. https://dx.doi.org/10.1016/S0024-3795(99)00062-2
  • Bayat, M., Teimoori, H., Pascal k−eliminated functional matrix and its property, Linear Algebra Appl., 308 (1–3) (2000), 65–75. https://dx.doi.org/10.1016/S0024-3795(99)00266-9
  • Call, G. S., Velleman, D. J., Pascal matrices, Amer. Math. Monthly, 100 (1993), 372–376. https://doi.org/10.1080/00029890.1993.11990415
  • Catalani, M., Identities for Tribonacci-related sequences, arXiv:math/0209179 [math.CO]. https://doi.org/10.48550/arXiv.math/0209179
  • Choi, E., Modular Tribonacci numbers by matrix method, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 20 (2013), 207–221. https://dx.doi.org/10.7468/jksmeb.2013.20.3.207
  • Devbhadra, S. V., Some Tribonacci identities, Math. Today, 27 (2011), 1–9.
  • Edelman, A., Strang, G., Pascal matrices, Amer. Math. Monthly, 111 (3) (2004), 189–197. https://dx.doi.org/10.1080/00029890.2004.11920065
  • Falcon, S., Plaza, A., On the Fibonacci k−numbers, Chaos, Solitons & Fractals, 32 (2007), 1615–1624. https://dx.doi.org/10.1016/j.chaos.2006.09.022
  • Falcon, S., On the k−Lucas Numbers, International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039–1050.
  • Feinberg, M., Fibonacci-Tribonacci, Fibonacci Quart., 1 (1963), 71–74.
  • Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quart., 3 (1965), 161–176.
  • Horadam, A. F., Special properties of the sequence $W_n(a, b; p, q)$, Fibonacci Quart., 5 (5) (1967), 424–434.
  • Horadam, A. F., Jacobsthal representation numbers, Fibonacci Quart., 34 (1) (1996), 40–53.
  • Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, New York, New Rochelle, Melbourne, Sydney, Second Edition, 2013.
  • Howard, F. T., A Tribonacci identity, Fibonacci Quart., 39 (2001), 352–357.
  • Jakubczyk, Z., Sums of Squares of Tribonacci Numbers, Advanced problems and solutions edited by Florian Luca, The Fibonacci Quarterly, August (2013), 4–5.
  • Kalman, D., Mena, R., The Fibonacci numbers-exposed, Math. Mag., 76 (3) (2003), 167–181. https://dx.doi.org/10.1080/0025570X.2003.11953176
  • Kızılateş, C., Terzioğlu, N., On r−min and r−max matrices, Journal of Applied Mathematics and Computing, (2022), 1–30. https://dx.doi.org/10.1007/s12190-022-01717-y
  • Kilic, E., Arikan, T., Studying new generalizations of Max-Min matrices with a novel approach, Turkish Journal of Mathematics, 43 (4) (2019), 2010–2024.
  • Pethe, S., Some identities for Tribonacci sequences, Fibonacci Quart., 26 (1988), 144–151.
  • Piezas, T., A tale of four constants, https://sites.google.com/site/tpiezas/0012.
  • Scott, A., Delaney, T., Hoggatt J. R., V., The Tribonacci sequence, Fibonacci Quart., 15 (1977), 193–200.
  • Spickerman, W., Binet’s formula for the Tribonacci sequence, Fibonacci Quart., 20 (1982), 118–120.
  • Williamson, R., Trotter, H., Multivariable Mathematics, second edition, Prentice-Hall, 1979.
  • Yalavigi, C. C., Properties of Tribonacci numbers, Fibonacci Quart., 10 (3) (1972), 231–246.
  • Yaying, T., Hazarika, B., On sequence spaces defined by the domain of a regular Tribonacci matrix, Mathematica Slovaca, 70 (3) (2020), 697–706. https://dx.doi.org/10.1515/ms-2017-0383
  • Zhang, Z., The linear algebra of the generalized Pascal matrix, Linear Algebra Appl., 250 (1997), 51–60. https://dx.doi.org/10.1016/0024-3795(95)00452-1
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Gonca Kızılaslan 0000-0003-1816-6095

Publication Date March 30, 2023
Submission Date January 3, 2022
Acceptance Date August 24, 2022
Published in Issue Year 2023 Volume: 72 Issue: 1

Cite

APA Kızılaslan, G. (2023). The linear algebra of a generalized Tribonacci matrix. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 72(1), 169-181. https://doi.org/10.31801/cfsuasmas.1052686
AMA Kızılaslan G. The linear algebra of a generalized Tribonacci matrix. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2023;72(1):169-181. doi:10.31801/cfsuasmas.1052686
Chicago Kızılaslan, Gonca. “The Linear Algebra of a Generalized Tribonacci Matrix”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72, no. 1 (March 2023): 169-81. https://doi.org/10.31801/cfsuasmas.1052686.
EndNote Kızılaslan G (March 1, 2023) The linear algebra of a generalized Tribonacci matrix. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72 1 169–181.
IEEE G. Kızılaslan, “The linear algebra of a generalized Tribonacci matrix”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 72, no. 1, pp. 169–181, 2023, doi: 10.31801/cfsuasmas.1052686.
ISNAD Kızılaslan, Gonca. “The Linear Algebra of a Generalized Tribonacci Matrix”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 72/1 (March 2023), 169-181. https://doi.org/10.31801/cfsuasmas.1052686.
JAMA Kızılaslan G. The linear algebra of a generalized Tribonacci matrix. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72:169–181.
MLA Kızılaslan, Gonca. “The Linear Algebra of a Generalized Tribonacci Matrix”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 72, no. 1, 2023, pp. 169-81, doi:10.31801/cfsuasmas.1052686.
Vancouver Kızılaslan G. The linear algebra of a generalized Tribonacci matrix. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2023;72(1):169-81.

Cited By

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https://doi.org/10.17678/beuscitech.1359202

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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