Analysing Bicomplex Matrices in Mathematica

Abstract

A bicomplex number is a composition of two complex numbers or four real numbers. However, a Bicomplex Matrix or a BC-Matrix is a  array of bicomplex numbers. Recently, studies on BC-matrices have caught interest of mathematicians where determinant and other properties have been explored. In present study on BC-matrices, mathematical computation software Mathematica has been applied and various examples and counterexamples are provided to substantiate the results. Step by step commands were given to find the determinant and Eigen values of a  BC-matrix for which rigorous calculations are needed, if the matrix is of higher order. In a particular case, Eigen values of a BC-matrix are obtained using single command for which we can verify the relationships between determinant, trace and the product of eigen values of the matrix. Eigen values by usual method (i.e., by solving the characteristic equation) have also been obtained and differences have been shown in both the outcomes. Unimodular Bicomplex matrices have been defined and an example for the same has been given and analyzed. Bicomplex numbers have found deep rooted applications in many areas of sciences, so this development may help in their applications with accuracy and much less time.