Note on Bicomplex Matrices

Canan Ölçek; Semra Kaya Nurkan

doi:10.36753/mathenot.476793

EN

Note on Bicomplex Matrices

Abstract

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.

Keywords

Complex number,Bicomplex number,Complex matrix,Bicomplex matrix

References

[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

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Canan Ölçek This is me
0000-0003-3079-3577

Semra Kaya Nurkan ^*
0000-0001-6473-4458

Publication Date

October 31, 2018

Submission Date

November 14, 2017

Acceptance Date

October 3, 2018

Published in Issue

Year 2018 Volume: 6 Number: 2

DOI

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

IZ

https://izlik.org/JA86NH93EJ

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

1.Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6(2):46-56. doi:10.36753/mathenot.476793

Chicago

Ölçek, Canan, and Semra Kaya Nurkan. 2018. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6 (2): 46-56. https://doi.org/10.36753/mathenot.476793.

EndNote

Ölçek C, Nurkan SK (October 1, 2018) Note on Bicomplex Matrices. Mathematical Sciences and Applications E-Notes 6 2 46–56.

IEEE

[1]C. Ölçek and S. K. Nurkan, “Note on Bicomplex Matrices”, Math. Sci. Appl. E-Notes, vol. 6, no. 2, pp. 46–56, Oct. 2018, doi: 10.36753/mathenot.476793.

ISNAD

Ölçek, Canan - Nurkan, Semra Kaya. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes 6/2 (October 1, 2018): 46-56. https://doi.org/10.36753/mathenot.476793.

JAMA

1.Ölçek C, Nurkan SK. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018;6:46–56.

MLA

Ölçek, Canan, and Semra Kaya Nurkan. “Note on Bicomplex Matrices”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 2, Oct. 2018, pp. 46-56, doi:10.36753/mathenot.476793.

Vancouver

1.Canan Ölçek, Semra Kaya Nurkan. Note on Bicomplex Matrices. Math. Sci. Appl. E-Notes. 2018 Oct. 1;6(2):46-5. doi:10.36753/mathenot.476793