Öz
Real quaternions have been expressed in terms of 4×4 matrices by means of Hamilton operators. These matrices are applied for rotations in Euclidean 4-space, and are determined also a Hamilton motions in E4. We study these matrices and show that the set of these matrices with the group operation of matrix multiplication is Lie group of 6-dimension.
Anahtar Kelimeler
De Moivre’s formula Homothetic motion Lie group Rotation Real quaternion
Kaynakça
- Adler, S. L. 1995. Quaternionic quantum mechanics and quantum fields. Oxford University Press Inc., New York. Pp. 65.
- Agrawal, O. P. 1987. Hamilton operators and dual-number-quaternions in spatial kinematics. Mechanism and Machine Theory 22 (6): 569-575.
- Farebrother, R. W., GroB, J. & Troschke, S. 2003. Matrix representation of quaternions. Linear Algebra and its Applications 362: 251-255.
- Groβ, J., Trenkler, G. & Troschke, S. 2001. Quaternions: futher contributions to a matrix oriented approach, Linear Algebra and its Applications 326: 205-213.
- Jafari, M., Mortazaasl, H. & Yayli, Y. 2011. De-Moivre’s formula for matrices of quaternions. JP Journal of Algebra, Number Theory and Applications 21(1): 57-67.
- Meinrenken E., Lie groups and Lie algebras, Lecture Notes, University of Toronto, 2010.
- Ward, J. P. 1997. Quaternions and Cayley numbers algebra and applications, Kluwer Academic Publishers, London. Pp.78.
- Weiner, J. L. & Wilkens, G. R. 2005. Quaternions and rotations in . Mathematical Association of America 12: 69-76.
- Yayli, Y. 1992. Homothetic motions at E
- 4,Mechanism and Machine
- Theory 27(3): 303-305.
- Yayli, Y. 1988. , Hamilton Motions and Lie Grups, Ph.D. Thesis, Gazi University, Ankara, Turkey.
- Zhang, F. 1997. Quaternions and matrices of quaternions. Linear Algebra and its Applications 251: 21-57.
Öz
Reel kuaterniyonlar Hamilton operatörleri aracılığıyla 4×4 matrisler cinsinden ifade edilmiştir. Bu matrisler Öklid 4-uzayda rotasyonlar için uygulanır ve aynı zamanda E4 bir Hamilton hareketleri tespit edilir. Biz bu matrisleri inceledik ve matris çarpımı grup ile bu matrislerin kümesi 6boyutun Lie grubu olduğunu göstermektedir
Anahtar Kelimeler
Kaynakça
- Adler, S. L. 1995. Quaternionic quantum mechanics and quantum fields. Oxford University Press Inc., New York. Pp. 65.
- Agrawal, O. P. 1987. Hamilton operators and dual-number-quaternions in spatial kinematics. Mechanism and Machine Theory 22 (6): 569-575.
- Farebrother, R. W., GroB, J. & Troschke, S. 2003. Matrix representation of quaternions. Linear Algebra and its Applications 362: 251-255.
- Groβ, J., Trenkler, G. & Troschke, S. 2001. Quaternions: futher contributions to a matrix oriented approach, Linear Algebra and its Applications 326: 205-213.
- Jafari, M., Mortazaasl, H. & Yayli, Y. 2011. De-Moivre’s formula for matrices of quaternions. JP Journal of Algebra, Number Theory and Applications 21(1): 57-67.
- Meinrenken E., Lie groups and Lie algebras, Lecture Notes, University of Toronto, 2010.
- Ward, J. P. 1997. Quaternions and Cayley numbers algebra and applications, Kluwer Academic Publishers, London. Pp.78.
- Weiner, J. L. & Wilkens, G. R. 2005. Quaternions and rotations in . Mathematical Association of America 12: 69-76.
- Yayli, Y. 1992. Homothetic motions at E
- 4,Mechanism and Machine
- Theory 27(3): 303-305.
- Yayli, Y. 1988. , Hamilton Motions and Lie Grups, Ph.D. Thesis, Gazi University, Ankara, Turkey.
- Zhang, F. 1997. Quaternions and matrices of quaternions. Linear Algebra and its Applications 251: 21-57.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Yazarlar | |
| Yayımlanma Tarihi | 25 Haziran 2015 |
| Yayımlandığı Sayı | Yıl 2015 Cilt: 8 Sayı: 1 |