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On the properties of quasi-quaternion Algebra

Year 2014, Volume: 63 Issue: 1, 1 - 10, 01.02.2014
https://doi.org/10.1501/Commua1_0000000700

Abstract

We study some fundamental properties of the quasi-quaternionsand derive the De Moivre’s and Euler’s formulae for matrices associated withthese quaternions. Furthermore, with the aid of the De-Moivre’s formula, anypowers of these matrices can be obtained

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, Appl. Math. Lett. Vol. 11, no. 6(1998)33-35
  • Ercan Z., Yuce S., On properties of the Dual Quaternions, European j. of Pure and Appl. Math., Vol. 4, no. 2(2011) 142-146
  • Farebrother R.W., GroB J., Troschke S., Matrix Representaion of Quaternions, Linear Algebra and its Appl., 362(2003)251-255
  • Jafari M., Mortazaasl H., Yayli Y., De Moivre’s Formula for Matrices of Quaternions, JP J. of Algebra, Number Theory and appl., Vol.21, no.1 (2011) 57-67
  • Kabadayi H., Yayli Y., De Moivre’s Formula for Dual Quaternions, Kuwait J. of Sci. & Tech., Vol. 38, no.1 (2011)15-23
  • Majernik V., Quaternion Formulation of the Galilean Space-Time Transformation, Acta phy. Slovaca, vol. 56, no.1(2006)9-14
  • Ozdemir M., The Roots of a Split Quaternion, Applied Math. Lett. 22(2009) 258-263
  • Rosenfeld b.a., Geometry of Lie Groups, Kluwer Academic Publishers, Dordrecht , 1997
  • Schmidt J. , Nieman H., Using Quaternions for Parametrizing 3-D Rotations in Uncon- strained Nonlinear Optimization, Vision Modeling and Visualization, Stuttgart, Germany (2001) 399–406
  • Ward J. P., Quaternions and Cayley Numbers Algebra and Applications, Kluwer Academic Publishers, London, 1997
  • Yayli Y., Homothetic Motions at E4. Mech. Mach. Theory, Vol. 27, no. 3 (1992)303-305 yayli y., Tutuncu E.E., Generalized Galilean Transformations and Dual Quaternions, Sci- entia Magna, Vol.5, no.1 (2009) 94-100
  • Zhang F., Quaternions and Matrices of Quaternions, Linear Algebra and its Appl., (1997) 21-57
  • Current address : Department of Mathematics, University College of Science and Technology Elm o Fan, Urmia, IRAN E-mail address : mjafari@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr/index.php?series=A1
Year 2014, Volume: 63 Issue: 1, 1 - 10, 01.02.2014
https://doi.org/10.1501/Commua1_0000000700

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, Appl. Math. Lett. Vol. 11, no. 6(1998)33-35
  • Ercan Z., Yuce S., On properties of the Dual Quaternions, European j. of Pure and Appl. Math., Vol. 4, no. 2(2011) 142-146
  • Farebrother R.W., GroB J., Troschke S., Matrix Representaion of Quaternions, Linear Algebra and its Appl., 362(2003)251-255
  • Jafari M., Mortazaasl H., Yayli Y., De Moivre’s Formula for Matrices of Quaternions, JP J. of Algebra, Number Theory and appl., Vol.21, no.1 (2011) 57-67
  • Kabadayi H., Yayli Y., De Moivre’s Formula for Dual Quaternions, Kuwait J. of Sci. & Tech., Vol. 38, no.1 (2011)15-23
  • Majernik V., Quaternion Formulation of the Galilean Space-Time Transformation, Acta phy. Slovaca, vol. 56, no.1(2006)9-14
  • Ozdemir M., The Roots of a Split Quaternion, Applied Math. Lett. 22(2009) 258-263
  • Rosenfeld b.a., Geometry of Lie Groups, Kluwer Academic Publishers, Dordrecht , 1997
  • Schmidt J. , Nieman H., Using Quaternions for Parametrizing 3-D Rotations in Uncon- strained Nonlinear Optimization, Vision Modeling and Visualization, Stuttgart, Germany (2001) 399–406
  • Ward J. P., Quaternions and Cayley Numbers Algebra and Applications, Kluwer Academic Publishers, London, 1997
  • Yayli Y., Homothetic Motions at E4. Mech. Mach. Theory, Vol. 27, no. 3 (1992)303-305 yayli y., Tutuncu E.E., Generalized Galilean Transformations and Dual Quaternions, Sci- entia Magna, Vol.5, no.1 (2009) 94-100
  • Zhang F., Quaternions and Matrices of Quaternions, Linear Algebra and its Appl., (1997) 21-57
  • Current address : Department of Mathematics, University College of Science and Technology Elm o Fan, Urmia, IRAN E-mail address : mjafari@science.ankara.edu.tr URL: http://communications.science.ankara.edu.tr/index.php?series=A1
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Mehdi Jafarı This is me

Publication Date February 1, 2014
Published in Issue Year 2014 Volume: 63 Issue: 1

Cite

APA Jafarı, M. (2014). On the properties of quasi-quaternion Algebra. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(1), 1-10. https://doi.org/10.1501/Commua1_0000000700
AMA Jafarı M. On the properties of quasi-quaternion Algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2014;63(1):1-10. doi:10.1501/Commua1_0000000700
Chicago Jafarı, Mehdi. “On the Properties of Quasi-Quaternion Algebra”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, no. 1 (February 2014): 1-10. https://doi.org/10.1501/Commua1_0000000700.
EndNote Jafarı M (February 1, 2014) On the properties of quasi-quaternion Algebra. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 1 1–10.
IEEE M. Jafarı, “On the properties of quasi-quaternion Algebra”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 63, no. 1, pp. 1–10, 2014, doi: 10.1501/Commua1_0000000700.
ISNAD Jafarı, Mehdi. “On the Properties of Quasi-Quaternion Algebra”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/1 (February 2014), 1-10. https://doi.org/10.1501/Commua1_0000000700.
JAMA Jafarı M. On the properties of quasi-quaternion Algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:1–10.
MLA Jafarı, Mehdi. “On the Properties of Quasi-Quaternion Algebra”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 63, no. 1, 2014, pp. 1-10, doi:10.1501/Commua1_0000000700.
Vancouver Jafarı M. On the properties of quasi-quaternion Algebra. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(1):1-10.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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