Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 72 Sayı: 1, 169 - 181, 30.03.2023

Gonca Kızılaslan

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

Öz

Kaynakça

  • 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

Yıl 2023, Cilt: 72 Sayı: 1, 169 - 181, 30.03.2023

Gonca Kızılaslan

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

Öz

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.

Anahtar Kelimeler

Tribonacci sequence factorization of matrices matrix exponential matrix inverse

Kaynakça

  • 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
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Gonca Kızılaslan 0000-0003-1816-6095

Yayımlanma Tarihi 30 Mart 2023
Gönderilme Tarihi 3 Ocak 2022
Kabul Tarihi 24 Ağustos 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 72 Sayı: 1

Kaynak Göster

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. Mart 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, sy. 1 (Mart 2023): 169-81. https://doi.org/10.31801/cfsuasmas.1052686.
EndNote Kızılaslan G (01 Mart 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., c. 72, sy. 1, ss. 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 (Mart 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, c. 72, sy. 1, 2023, ss. 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

A GENERALIZATION OF THE REGULAR TRIBONACCI-LUCAS MATRIX
Bitlis Eren University Journal of Science and Technology
https://doi.org/10.17678/beuscitech.1359202

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

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