Matrices with Hyperbolic Number Entries
Yıl: 2022 Cilt: 14 Sayı: 2 Sayfa Aralığı: 306 - 313 Metin Dili: İngilizce DOI: 10.47000/tjmcs.1071829 İndeks Tarihi: 17-01-2023
Matrices with Hyperbolic Number Entries
Öz: In this study, firstly, we will present some properties of hyperbolic numbers. Then, we will introduce hyperbolic matrices, which are matrices with hyperbolic number entries. Additionally, we will examine the algebraic properties of these matrices and reveal its difference from other matrix structures such as real, dual, and complex matrices. As a result of comparing the results found in this work with real, dual, and complex matrices, it will be revealed that there are similarities in additive properties and differences in some multiplicative properties. Finally, we will define some special hyperbolic matrices and give their properties and relations with real matrices.
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Alag ̈oz, Y., Oral, K.H., Y ̈uce, S., Split quaternion matrices, Miskolc Mathematical Notes, 13(2)(2012), 223–232.
- [2] Assis, A.K.T., Perplex numbers and quaternions, International Journal of Mathematical Education in Science and Technology, 22(4)(1991), 555–562.
- [3] Beauregard, R.A., Suryanarayan E.R., Pythagorean triples: the hyperbolic view, The College Mathematics Journal, 27(3)(1996), 170–181.
- [4] Da ̆gdeviren, A., K ̈ur ̈uz, F., Special real and dual matrices with Hadamard product, Journal of Engineering Technology and Applied Sciences, 6(2)(2021), 127–134.
- [5] Da ̆gdeviren, A., Lorentz matris carpimi ve dual matrislerin ozellikleri, Master’s Thesis, Yildiz Technical University, 2013.
- [6] Fjelstad, P., Extending special relativity via the perplex numbers, American Journal of Physics, 54(5)(1986), 416–422.
- [7] Gutin, R., Matrix decompositions over the split-complex numbers, arXiv preprint arXiv:2105.08047, (2021).
- [8] Kulyabov, D.S., Korolkova, A.V., Gevorkyan, M.N., Hyperbolic numbers as Einstein numbers, In Journal of Physics: Conference Series, IOP Publishing, 1557(1)(2020), 12–27.
- [9] Motter, A.E., Rosa, M.A.F., Hyperbolic calculus, Advances in Applied Clifford Algebras, 8(1)(1998), 109–128.
- [10] Petroudi, S.H.J., Pirouz, M., Akbiyik, M., Yilmaz, F., Some special matrices with harmonic numbers, Konuralp Journal of Mathematics 10(1)(2022), 188–196.
- [11] Sobczyk, G., The hyperbolic number plane, The College Mathematics Journal, 26(4)(1995), 268–280.
- [12] Stanimirovi ́c, P., Nikolov, J., Stanimirovi ́c, I., A generalization of Fibonacci and Lucas matrices, Discrete Applied Mathematics, 156(14)(2008), 2606–2619.
- [13] Yaglom, I.M., Complex Numbers in Geometry, Academic Press, 2014.
| APA | Kürüz F, Dağdeviren A (2022). Matrices with Hyperbolic Number Entries. , 306 - 313. 10.47000/tjmcs.1071829 |
| Chicago | Kürüz Ferhat,Dağdeviren Ali Matrices with Hyperbolic Number Entries. (2022): 306 - 313. 10.47000/tjmcs.1071829 |
| MLA | Kürüz Ferhat,Dağdeviren Ali Matrices with Hyperbolic Number Entries. , 2022, ss.306 - 313. 10.47000/tjmcs.1071829 |
| AMA | Kürüz F,Dağdeviren A Matrices with Hyperbolic Number Entries. . 2022; 306 - 313. 10.47000/tjmcs.1071829 |
| Vancouver | Kürüz F,Dağdeviren A Matrices with Hyperbolic Number Entries. . 2022; 306 - 313. 10.47000/tjmcs.1071829 |
| IEEE | Kürüz F,Dağdeviren A "Matrices with Hyperbolic Number Entries." , ss.306 - 313, 2022. 10.47000/tjmcs.1071829 |
| ISNAD | Kürüz, Ferhat - Dağdeviren, Ali. "Matrices with Hyperbolic Number Entries". (2022), 306-313. https://doi.org/10.47000/tjmcs.1071829 |
| APA | Kürüz F, Dağdeviren A (2022). Matrices with Hyperbolic Number Entries. Turkish Journal of Mathematics and Computer Science, 14(2), 306 - 313. 10.47000/tjmcs.1071829 |
| Chicago | Kürüz Ferhat,Dağdeviren Ali Matrices with Hyperbolic Number Entries. Turkish Journal of Mathematics and Computer Science 14, no.2 (2022): 306 - 313. 10.47000/tjmcs.1071829 |
| MLA | Kürüz Ferhat,Dağdeviren Ali Matrices with Hyperbolic Number Entries. Turkish Journal of Mathematics and Computer Science, vol.14, no.2, 2022, ss.306 - 313. 10.47000/tjmcs.1071829 |
| AMA | Kürüz F,Dağdeviren A Matrices with Hyperbolic Number Entries. Turkish Journal of Mathematics and Computer Science. 2022; 14(2): 306 - 313. 10.47000/tjmcs.1071829 |
| Vancouver | Kürüz F,Dağdeviren A Matrices with Hyperbolic Number Entries. Turkish Journal of Mathematics and Computer Science. 2022; 14(2): 306 - 313. 10.47000/tjmcs.1071829 |
| IEEE | Kürüz F,Dağdeviren A "Matrices with Hyperbolic Number Entries." Turkish Journal of Mathematics and Computer Science, 14, ss.306 - 313, 2022. 10.47000/tjmcs.1071829 |
| ISNAD | Kürüz, Ferhat - Dağdeviren, Ali. "Matrices with Hyperbolic Number Entries". Turkish Journal of Mathematics and Computer Science 14/2 (2022), 306-313. https://doi.org/10.47000/tjmcs.1071829 |
