Year 2015,
Volume: 36 Issue: 5, 103 - 112, 19.03.2015
Abstract
Abstract. By representing semi-quaternions as four-dimensional vectors and
the multiplication of quaternions as matrix-by-vector product, we investi-
gate properties of matrix associated with a semi-quaternion and examine De-
Moivre's formula for this matrix, from which the nth power of such a matrix
can be determined.
References
- Adler S. L., Quaternionic quantum mechanics and quantum …elds, Oxford University Press inc., New York, 1995.
- Agrawal O. P., Hamilton operators and dual-number-quaternions in spatial kinematics, Mech. Mach. Theory. 22,no.6 (1987)569-575
- Cho E., De-Moivre Formula for Quaternions, Applied Mathematics Letters, 11(6) (1998)33- 35
- Dyachkova M., On Hopf bundle analogue for semiquaternion algebra, 10thInternational Conference DGA, Olomouc, Czech Republic, 2007.
- Farebrother R.W., GroB J., Troschke S., Matrix Representaion of Quaternions, Linear Algebra and its Application, 362(2003)251-255
- Hamilton W.R., Lecture on Quaternions, Dublin : Hodges and Smith, 1853.
- Jafari M., Mortazaasl H., Yayli Y., De Moivre’s Formula for Matrices of Quaternions, JP Journal of Algebra, Number Theory and appllication, Vol. 21, no.1 (2011) 57-67.
- Jafari M., Meral M., Yayli Y., Matrix Representaion of Dual Quaternions, Gazi Univer- sity of Science, 26(4) (2013) 535-542.
- Kabadayi H., Yayli Y., De Moivre’s Formula for Dual Quaternions, Kuwait Journal of Sci. &Tech., Vol. 38, no.1 (2011)15-23
- Mamagani B.A, Jafari M., Some Notes on Matrix of Generalized Quaternions, Interna- tional Research Journal of Applied and Basic Science, Vol. 7(14) (2013) 1086-1093.
- Mamagani B.A, Jafari M., On properties of Generalized Quaternion Algebra, Journal of Novel Applied Science, Vol. 12/2: 683-689. Mortazaasl H.,Jafari M., Yayli Y., Some Algebraic Properties of Dual Generalized Quaternions, Far East Journal of Mathematical Science, Vol. 69(2) (2012) 307-318.
- Mortazaasl H., Jafari M., A Study on Semi-Quaternions Algebra in Semi-Euclidean 4- Space, Mathematical Science and Application E-Notes, Vol. 1 (2) (2013) 20-27.
- Ozdemir M., The Roots of a Split Quaternion, Applied Mathematic Letters, 22(2009) 258- 263
- Ward J. P., Quaternions and Cayley Numbers Algebra and Applications, Kluwer Academic Publishers, London, 1997
- Yayli Y., Homothetic Motions at E. Mech. Mach. Theory, Vol. 27, no. 3 (1992)303-305
- Zhang F., Quaternions and Matrices of Quaternions, Linear Algebra and its Applications, 251(1997) 21-57
Year 2015,
Volume: 36 Issue: 5, 103 - 112, 19.03.2015
Abstract
References
- Adler S. L., Quaternionic quantum mechanics and quantum …elds, Oxford University Press inc., New York, 1995.
- Agrawal O. P., Hamilton operators and dual-number-quaternions in spatial kinematics, Mech. Mach. Theory. 22,no.6 (1987)569-575
- Cho E., De-Moivre Formula for Quaternions, Applied Mathematics Letters, 11(6) (1998)33- 35
- Dyachkova M., On Hopf bundle analogue for semiquaternion algebra, 10thInternational Conference DGA, Olomouc, Czech Republic, 2007.
- Farebrother R.W., GroB J., Troschke S., Matrix Representaion of Quaternions, Linear Algebra and its Application, 362(2003)251-255
- Hamilton W.R., Lecture on Quaternions, Dublin : Hodges and Smith, 1853.
- Jafari M., Mortazaasl H., Yayli Y., De Moivre’s Formula for Matrices of Quaternions, JP Journal of Algebra, Number Theory and appllication, Vol. 21, no.1 (2011) 57-67.
- Jafari M., Meral M., Yayli Y., Matrix Representaion of Dual Quaternions, Gazi Univer- sity of Science, 26(4) (2013) 535-542.
- Kabadayi H., Yayli Y., De Moivre’s Formula for Dual Quaternions, Kuwait Journal of Sci. &Tech., Vol. 38, no.1 (2011)15-23
- Mamagani B.A, Jafari M., Some Notes on Matrix of Generalized Quaternions, Interna- tional Research Journal of Applied and Basic Science, Vol. 7(14) (2013) 1086-1093.
- Mamagani B.A, Jafari M., On properties of Generalized Quaternion Algebra, Journal of Novel Applied Science, Vol. 12/2: 683-689. Mortazaasl H.,Jafari M., Yayli Y., Some Algebraic Properties of Dual Generalized Quaternions, Far East Journal of Mathematical Science, Vol. 69(2) (2012) 307-318.
- Mortazaasl H., Jafari M., A Study on Semi-Quaternions Algebra in Semi-Euclidean 4- Space, Mathematical Science and Application E-Notes, Vol. 1 (2) (2013) 20-27.
- Ozdemir M., The Roots of a Split Quaternion, Applied Mathematic Letters, 22(2009) 258- 263
- Ward J. P., Quaternions and Cayley Numbers Algebra and Applications, Kluwer Academic Publishers, London, 1997
- Yayli Y., Homothetic Motions at E. Mech. Mach. Theory, Vol. 27, no. 3 (1992)303-305
- Zhang F., Quaternions and Matrices of Quaternions, Linear Algebra and its Applications, 251(1997) 21-57
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences Research Article |
| Authors | |
| Publication Date | March 19, 2015 |
| Published in Issue | Year 2015 Volume: 36 Issue: 5 |