Certain Results on Bicomplex Matrices

1
Anjali Sharma
Anjali Sharma
2
Amita Sharma
Amita Sharma
1 Institute of basic Science,Khandari, Dr. B.R. Ambedkar University, Agra-282002 (India)

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This paper begins the study of bicomplex matrices. In this paper, we have defined bicomplex matrices, determinant of a bicomplex square matrix and singular and non-singular matrices in C 2 . We have proved that the set of all bicomplex square matrices of order n is an algebra. We have given some definitions and results regarding adjoint and inverse of a matrix in C 2 . We have defined three types of conjugates and three types of tranjugates of a bicomplex matrix. With the help of these conjugates and tranjugates, we have also defined symmetric and skew -symmetric matrices, Hermitian and Skew -Hermitian matrices in C 2 .

10 Cites in Articles

References

  1. D Rochon,M Shapiro (2004). On Algebraic Properties of Bicomplex and Hyperbolic Numbers.
  2. M Futagawa (1928). On the theory of functions of a quaternary Variable.
  3. M Futagawa (1932). On the theory of functions of a quaternary Variable, II.
  4. S Lipschutz,M Lipson,Schaum (2005). Outline of Theory and Problem of linear Algebra˝ Tata McGraw.
  5. G Price (1991). An introduction to multicomplex spaces and Functions.
  6. James Riley (1953). Contributions to the theory of functions of a bicomplex variable.
  7. F Ringleb (1933). Beitrage Zur Funktionen theorie in Hyperkomplexon Systemen, I.
  8. C Segre (1892). Le Rappresentazioni Reali Delle Forme Complesse e Gli enti Iperalgebrici.
  9. Rajiv Srivastava (2003). Bicomplex Numbers: Analysis and applications.
  10. Rajiv Srivastava (2008). Certain topological aspects of Bicomplex space.

Funding

No external funding was declared for this work.

Conflict of Interest

The authors declare no conflict of interest.

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No ethics committee approval was required for this article type.

Data Availability

Not applicable for this article.

Anjali Sharma. 2018. \u201cCertain Results on Bicomplex Matrices\u201d. Global Journal of Science Frontier Research - F: Mathematics & Decision GJSFR-F Volume 18 (GJSFR Volume 18 Issue F2): .

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Classification: MSC : 15 B 57 , 30 G 35
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v1.2

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March 5, 2018

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English

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This paper begins the study of bicomplex matrices. In this paper, we have defined bicomplex matrices, determinant of a bicomplex square matrix and singular and non-singular matrices in C 2 . We have proved that the set of all bicomplex square matrices of order n is an algebra. We have given some definitions and results regarding adjoint and inverse of a matrix in C 2 . We have defined three types of conjugates and three types of tranjugates of a bicomplex matrix. With the help of these conjugates and tranjugates, we have also defined symmetric and skew -symmetric matrices, Hermitian and Skew -Hermitian matrices in C 2 .

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Certain Results on Bicomplex Matrices

Anjali Sharma
Anjali Sharma Institute of basic Science,Khandari, Dr. B.R. Ambedkar University, Agra-282002 (India)
Amita Sharma
Amita Sharma

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