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Note on Bicomplex Matrices

Yıl 2018, Cilt: 6 Sayı: 2, 46 - 56, 31.10.2018

Canan Ölçek Semra Kaya Nurkan

https://doi.org/10.36753/mathenot.476793

Öz

In this paper, we consider bicomplex numbers and bicomplex matrices. Firstly, we give some properties
of bicomplex numbers.After that we investigate bicomplex matrices using properties of complex matrices.
Then we define the complex adjoint matrix of bicomplex matrices and we describe some of their
properties. Furthermore, we give the definition of q-determinant of bicomplex matrices.

Anahtar Kelimeler

Complex number Bicomplex number Complex matrix Bicomplex matrix

Kaynakça

  • [1] Y. Alagöz, K. H. Oral, and S. Yüce, "Split quaternion matrices", Miskolc Mathematical Notes vol.13(2012), No.2, p.223-232
  • [2] G.Baley Price, An ˙Introduction to multicomplex spaces and functions, 1991, Monographs and textbooks inpure and applied mathematics, v.140;Marcel Gekker, Inc., 402 pp
  • [3] F.O.Farid ,Qing-Wen Wang and F. Zhang, "On the eigenvalues of quaternion matrices", Linear and Multilinear Algebra vol.59, no.4, April 2011, 451-473
  • [4] H. Kaya, "Genelle¸stirilmi¸s Bikompleks sayılar" , Yüksek Lisans Tezi , Bilecik ¸Seyh Edebali Üniverstesi, Bilecik, 2014
  • [5] M.E.Luna-Elizarraras, M.Shapiro, D.C. Struppa, A.Vajiac, "Bicomplex Numbers and their elementary functions CUBO". A Mathematical Journal vol.14, No:02, (61-80). June, 2012
  • [6] M. Özdemir, M. Erdo˘gdu and H. ¸Sim¸sek, "On the Eigen values and Eigenvectors of a Lorentzion Rotation Matrix by using split queternions". Adv.Appl. Clifford Algebras 24(2014), 179-192
  • [7] D.Rochon, M.Shapiro, "On algebraic properties of bicomplex and hyperbolic numbers", an. Univ. Oredea Fasc. Mat. 11 (2004) 71-110
  • [8] T. Ünal, "Kuaterniyonlar ve Kuaterniyon Matrisleri" , Yüksek Lisans Tezi, Dumlupınar Üniversitesi, Haziran, 2011.
  • [9] F. Zhang ,"Quaternions and Matrices of Quaternions" Linear Algebra Appl., vol 251, pp.21-57, 1997

Yıl 2018, Cilt: 6 Sayı: 2, 46 - 56, 31.10.2018

Canan Ölçek Semra Kaya Nurkan

https://doi.org/10.36753/mathenot.476793

Öz

Kaynakça

  • [1] Y. Alagöz, K. H. Oral, and S. Yüce, "Split quaternion matrices", Miskolc Mathematical Notes vol.13(2012), No.2, p.223-232
  • [2] G.Baley Price, An ˙Introduction to multicomplex spaces and functions, 1991, Monographs and textbooks inpure and applied mathematics, v.140;Marcel Gekker, Inc., 402 pp
  • [3] F.O.Farid ,Qing-Wen Wang and F. Zhang, "On the eigenvalues of quaternion matrices", Linear and Multilinear Algebra vol.59, no.4, April 2011, 451-473
  • [4] H. Kaya, "Genelle¸stirilmi¸s Bikompleks sayılar" , Yüksek Lisans Tezi , Bilecik ¸Seyh Edebali Üniverstesi, Bilecik, 2014
  • [5] M.E.Luna-Elizarraras, M.Shapiro, D.C. Struppa, A.Vajiac, "Bicomplex Numbers and their elementary functions CUBO". A Mathematical Journal vol.14, No:02, (61-80). June, 2012
  • [6] M. Özdemir, M. Erdo˘gdu and H. ¸Sim¸sek, "On the Eigen values and Eigenvectors of a Lorentzion Rotation Matrix by using split queternions". Adv.Appl. Clifford Algebras 24(2014), 179-192
  • [7] D.Rochon, M.Shapiro, "On algebraic properties of bicomplex and hyperbolic numbers", an. Univ. Oredea Fasc. Mat. 11 (2004) 71-110
  • [8] T. Ünal, "Kuaterniyonlar ve Kuaterniyon Matrisleri" , Yüksek Lisans Tezi, Dumlupınar Üniversitesi, Haziran, 2011.
  • [9] F. Zhang ,"Quaternions and Matrices of Quaternions" Linear Algebra Appl., vol 251, pp.21-57, 1997
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Canan Ölçek 0000-0003-3079-3577

Semra Kaya Nurkan 0000-0001-6473-4458

Yayımlanma Tarihi 31 Ekim 2018
Gönderilme Tarihi 14 Kasım 2017
Kabul Tarihi 3 Ekim 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 6 Sayı: 2

Kaynak Göster

APA Ölçek, C., & Nurkan, S. K. (2018). Note on Bicomplex Matrices. Mathematical Sciences and Applications E-Notes, 6(2), 46-56. https://doi.org/10.36753/mathenot.476793
AMA Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. Ekim 2018;6(2):46-56. doi:10.36753/mathenot.476793
Chicago Ölçek, Canan, ve Semra Kaya Nurkan. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6, sy. 2 (Ekim 2018): 46-56. https://doi.org/10.36753/mathenot.476793.
EndNote Ölçek C, Nurkan SK (01 Ekim 2018) Note on Bicomplex Matrices. Mathematical Sciences and Applications E-Notes 6 2 46–56.
IEEE C. Ölçek ve S. K. Nurkan, “Note on Bicomplex Matrices”, Math. Sci. Appl. E-Notes, c. 6, sy. 2, ss. 46–56, 2018, doi: 10.36753/mathenot.476793.
ISNAD Ölçek, Canan - Nurkan, Semra Kaya. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6/2 (Ekim 2018), 46-56. https://doi.org/10.36753/mathenot.476793.
JAMA Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6:46–56.
MLA Ölçek, Canan ve Semra Kaya Nurkan. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes, c. 6, sy. 2, 2018, ss. 46-56, doi:10.36753/mathenot.476793.
Vancouver Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6(2):46-5.

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