Certain Results on Bicomplex Matrices
bicomplex matrices, conjugates matrices, tranjugate matrices, hermitian matrices, skew hermitian matrices
Abstract
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 .
Downloads
How to Cite
References
D Rochon, M Shapiro (2004) On Algebraic Properties of Bicomplex and Hyperbolic Numbers. 11, 71-110.
M Futagawa (1928) On the theory of functions of a quaternary Variable. 29, 175-222.
M Futagawa (1932) On the theory of functions of a quaternary Variable, II. 35, 69-120.
S Lipschutz, M Lipson, Schaum (2005) Outline of Theory and Problem of linear Algebra˝ Tata McGraw.
G Price (1991) An introduction to multicomplex spaces and Functions.
James Riley (1953) Contributions to the theory of functions of a bicomplex variable. 5(2), 132-165.
F Ringleb (1933) Beitrage Zur Funktionen theorie in Hyperkomplexon Systemen, I. 57, 311-340.
C Segre (1892) Le Rappresentazioni Reali Delle Forme Complesse e Gli enti Iperalgebrici. 40, 413-467.
Rajiv Srivastava (2003) Bicomplex Numbers: Analysis and applications. 72(1-4), 69-87.
Rajiv Srivastava (2008) Certain topological aspects of Bicomplex space.
Published
2018-03-05
Issue
Section
License
Copyright (c) 2018 Authors and Global Journals Private Limited
This work is licensed under a Creative Commons Attribution 4.0 International License.