Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications

Özen, Kahraman Esen; Tosun, Murat

Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications

Kahraman Esen ÖZEN, (Sakarya Üniversitesi, Matematik Bölümü, Sakarya, Türkiye)

Murat TOSUN (Sakarya Üniversitesi, Matematik Bölümü, Sakarya, Türkiye)

International Electronic Journal of Geometry

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Yıl: 2018 Cilt: 11 Sayı: 2 Sayfa Aralığı: 96 - 103 Metin Dili: İngilizce İndeks Tarihi: 01-08-2019

Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications

Öz:

In this study, we obtain the 4 × 4 elliptic matrix representations of elliptic biquaternions with theaid of the left and right Hamilton operators. Afterwards, we show that the space of 4 × 4 matricesgenerated by left Hamilton operator is isomorphic to the space of elliptic biquaternions. Then, westudy the De-Moivre’s and Euler formulas for the matrices of this matrix space. Additionally, thepowers of these matrices are obtained with the aid of the De-Moivre’s formula.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

van der Waerden, B. L., Hamilton’s discovery of quaternions. Math. Mag. 49 (1976), no. 5, 227-234.
Zhang, F., Quaternions and matrices of quaternions. Linear Algebra and its Applications 251 (1997), 21-57.
Grob, J., Trenkler, G. and Troschke, S.-O., Quaternions: further contributions to a matrix oriented approach. Linear Algebra and its Applications 326 (2001), 205-213.
Farebrother, R. W., Grob, J. and Troschke, S.-O., Matrix representation of quaternions. Linear Algebra and its Applications 362 (2003), 251-255.
Cho, E., De-Moivre’s formula for Quaternions. Appl. Math. Lett. 11 (1998), no. 6, 33-35.
Jafari, M., Mortazaasl, H. and Yaylı, Y., De Moivre’s formula for matrices of quaternions. JP Journal of Algebra, Number Theory and Applications 21 (2011), no. 1, 57-67.
Hamilton, W. R., Lectures on quaternions. Hodges and Smith, Dublin, 1853.
Jafari, M., On the matrix algebra of complex quaternions. Accepted for publication in TWMS Journal of Pure and Applied Mathematics (2016), DOI: 10.13140/RG.2.1.3565.2321.
Agrawal, O. P., Hamilton operators and dual-number-quaternions in spatial kinematics. Mech. Mach. Theory 22 (1987), no. 6, 569-575.
Yaylı, Y., Homothetic motions at E 4 . Mech. Mach. Theory 27 (1992), no. 3, 303-305.
Güngör, M. A. and Sarduvan, M., A note on dual quaternions and matrices of dual quaternions. Scientia Magna 7 (2011), no. 1, 1-11.
Kösal, H. H. and Tosun, M., Commutative quaternion matrices. Adv. Appl. Clifford Alg. 24 (2014), no. 3, 769-779.
Akyig̃it, M., Kösal, H. H. and Tosun, M., A Note on matrix representations of split quaternions. Journal of Advanced Research in Applied Mathematics 7 (2015), no. 2, 26-39.
Özen, K. E. and Tosun, M., Elliptic biquaternion algebra. AIP Conf. Proc. 1926 (2018), 020032-1–020032-6, https://doi.org/10.1063/1.5020481.
Özen, K. E. and Tosun, M., A note on elliptic biquaternions. AIP Conf. Proc. 1926 (2018), 020033-1–020033-6, https://doi.org/10.1063/1.5020482.
Özen, K. E. and Tosun, M., p-Trigonometric approach to elliptic biquaternions. Adv. Appl. Clifford Alg. 28:62 (2018), https://doi.org/10.1007/s00006-018-0878-3.
Harkin, A. A. and Harkin, J. B., Geometry of generalized complex numbers. Math. Mag. 77 (2004), no. 2, 118-129.
Kösal, H. H., On commutative quaternion matrices. Sakarya University, Graduate School of Natural and Applied Sciences, Sakarya, Ph.D. Thesis, 2016.

APA	Özen K, Tosun M (2018). Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. , 96 - 103.
Chicago	Özen Kahraman Esen,Tosun Murat Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. (2018): 96 - 103.
MLA	Özen Kahraman Esen,Tosun Murat Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. , 2018, ss.96 - 103.
AMA	Özen K,Tosun M Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. . 2018; 96 - 103.
Vancouver	Özen K,Tosun M Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. . 2018; 96 - 103.
IEEE	Özen K,Tosun M "Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications." , ss.96 - 103, 2018.
ISNAD	Özen, Kahraman Esen - Tosun, Murat. "Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications". (2018), 96-103.

APA	Özen K, Tosun M (2018). Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. International Electronic Journal of Geometry, 11(2), 96 - 103.
Chicago	Özen Kahraman Esen,Tosun Murat Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. International Electronic Journal of Geometry 11, no.2 (2018): 96 - 103.
MLA	Özen Kahraman Esen,Tosun Murat Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. International Electronic Journal of Geometry, vol.11, no.2, 2018, ss.96 - 103.
AMA	Özen K,Tosun M Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. International Electronic Journal of Geometry. 2018; 11(2): 96 - 103.
Vancouver	Özen K,Tosun M Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications. International Electronic Journal of Geometry. 2018; 11(2): 96 - 103.
IEEE	Özen K,Tosun M "Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications." International Electronic Journal of Geometry, 11, ss.96 - 103, 2018.
ISNAD	Özen, Kahraman Esen - Tosun, Murat. "Elliptic Matrix Representations of Elliptic Biquaternions and Their Applications". International Electronic Journal of Geometry 11/2 (2018), 96-103.