C,H,O-Katsayılı Sedeniyonların Özel Matris Gösterimleri ve Bazı Özellikleri

Bu makalede ilk olarak sedeniyonlar ile ilgili temel kavramlar verilmiştir. Daha sonra sedeniyonların kompleks (C), kuaterniyon (H) ve oktoniyon (O) katsayılı gösterimlerinden yararlanılarak farklı türden eşlenikleri tanımlanıp, bazı özellikleri verilecektir. Son olarak da sedeniyonların ℂ,ℍ,?-katsayılı özel matris gösterimleri sunulacaktır.

Some Properties and Special Matrix Representations of ℂ, ℍ, ?- Coefficient Sedenion Numbers

In this article, firstly, the basic concepts about the sedenions are given. Then, using the representations of the sedenions with complex (ℂ), quaternion (ℍ) and octonion (O) coefficients, different types of conjugates will be defined and some properties will be given. Finally, ℂ, H, ? -coefficient special matrix representations of sedenions will be presented.

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  • [1] Kim J. E., Ha S.J., Shon K.H. 2014. Properties of hyperholomorphic functions on dual sedenion numbers. Honam Mathematical Journal, 36 (4): 921-932.
  • [2] Imaeda K., Imaeda M. 2000. Sedenions: algebra and analysis. Applied Mathematics and Computation, 115: 77-88.
  • [3] Carmody K. 1997. Circular and hyperbolic quaternions, octonions, and sedenions further results. Applied Mathematics and Computation, 84 (1): 27-47.
  • [4] Messelmi F. 2015. Dual-complex numbers and their holomorphic functions. https://hal.archivesouvertes.fr (Erişim Tarihi: 20.01.2021).
  • [5] Carmody K. 1988. Circular and hyperbolic quaternions, octonions, and sedenions. Applied Mathematics and Computation, 28 (1):47-72.
  • [6] Taşyurdu Y., Akpınar A. 2020. Perrin octonions and Perrin sedenions. Konuralp Journal of Mathematics, 8 (2): 384-390.
  • [7] Soykan Y., Okumuş İ., Taşdemir E. 2020. On generalized tribonacci sedenions. Sarajevo Journal of Mathematics, 16 (1): 103-122.
  • [8] Catarino P. (2019). k-Pell, k-Pell–Lucas and modified k-Pell sedenions. Asian-European Journal of Mathematics, 12 (2):1950018.
  • [9] Bilgici G., Tokeser Ü., Ünal Z. 2017. Fibonacci and Lucas Sedenions. Journal of Integer Sequences, 20 (1): 17-18.
  • [10] Degtereva M. P. On some properties of sedenions. Doklady Akademii Nauk, 67:965-967.
  • [11] Sorgsepp L., Lohmus J. 1981. Binary and ternary sedenions. Hadronic Journal, 4 (2), 327-353.
  • [12] Müller H.E. Hypercomplex numbers and their matrix representations. https://herbert-mueller.info (Erişim Tarihi: 15.11.2020).
  • [13] Okubo S. 1995. Introduction to Octonion and Other Non-associative Algebras in Physics, Cambridge University Press, Cambridge.
  • [14] Baez J. 2002. The octonions, Bulletin of American Mathematical Society, 39 (2): 145-205.
  • [15] Tanışlı M., Kansu, M.E. 2011. Octonionic Maxwell's equations for bi-isotropic media. Journal of Mathematical Physics, 52: (5), 053511.
  • [16] Cawagas R.E., Carrascal A.S., Bautista L.A., Maria J., Urrutia J.D., Nobles B.G. 2009. The Subalgebra Structure of the Cayley-Dickson Algebra of Dimension 32 (trigintaduonion) https://arxiv.org/abs/0907.2047 (Erişim Tarihi: 20.01.2021).