BibTex RIS Kaynak Göster

SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS

Yıl 2015, Cilt: 36 Sayı: 5, 103 - 112, 19.03.2015
https://doi.org/10.17776/csj.04266

Öz

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.

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, 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
Yıl 2015, Cilt: 36 Sayı: 5, 103 - 112, 19.03.2015
https://doi.org/10.17776/csj.04266

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, 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
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Fen Bilimleri Makalesi
Yazarlar

Mehdi Jafarı

Habib Molaeı Bu kişi benim

Yayımlanma Tarihi 19 Mart 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 36 Sayı: 5

Kaynak Göster

APA Jafarı, M., & Molaeı, H. (2015). SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(5), 103-112. https://doi.org/10.17776/csj.04266
AMA Jafarı M, Molaeı H. SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. Ağustos 2015;36(5):103-112. doi:10.17776/csj.04266
Chicago Jafarı, Mehdi, ve Habib Molaeı. “SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, sy. 5 (Ağustos 2015): 103-12. https://doi.org/10.17776/csj.04266.
EndNote Jafarı M, Molaeı H (01 Ağustos 2015) SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 5 103–112.
IEEE M. Jafarı ve H. Molaeı, “SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, c. 36, sy. 5, ss. 103–112, 2015, doi: 10.17776/csj.04266.
ISNAD Jafarı, Mehdi - Molaeı, Habib. “SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/5 (Ağustos 2015), 103-112. https://doi.org/10.17776/csj.04266.
JAMA Jafarı M, Molaeı H. SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:103–112.
MLA Jafarı, Mehdi ve Habib Molaeı. “SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, c. 36, sy. 5, 2015, ss. 103-12, doi:10.17776/csj.04266.
Vancouver Jafarı M, Molaeı H. SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(5):103-12.