BibTex RIS Kaynak Göster

On the properties of quasi-quaternion Algebra

Yıl 2014, Cilt: 63 Sayı: 1, 1 - 10, 01.02.2014
https://doi.org/10.1501/Commua1_0000000700

Öz

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

Kaynakça

  • 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
Yıl 2014, Cilt: 63 Sayı: 1, 1 - 10, 01.02.2014
https://doi.org/10.1501/Commua1_0000000700

Öz

Kaynakça

  • 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
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Mehdi Jafarı Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 63 Sayı: 1

Kaynak Göster

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. Şubat 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, sy. 1 (Şubat 2014): 1-10. https://doi.org/10.1501/Commua1_0000000700.
EndNote Jafarı M (01 Şubat 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., c. 63, sy. 1, ss. 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 (Şubat 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, c. 63, sy. 1, 2014, ss. 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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