BibTex RIS Kaynak Göster

SOME PROPERTIES OF MATRIX ALGEBRA OF SEMI-QUATERNIONS

Yıl 2015, Cilt: 36 Sayı: 5, 103 - 112, 19.03.2015

Mehdi Jafarı , Habib Molaeı

https://doi.org/10.17776/csj.04266
Cited By: 1

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.

Anahtar Kelimeler

De Moivre’s formula Hamilton operator semi-quaternion

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

Mehdi Jafarı , Habib Molaeı

https://doi.org/10.17776/csj.04266
Cited By: 1

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

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.

Cited By

Similarity and Semi-similarity Relations on the Degenerate Quaternions, Pseudodegenerate Quaternions and Doubly Degenerate Quaternions
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Abdullah Inalcik
https://doi.org/10.1007/s00006-016-0674-x