Some New Properties of The Real Quaternion Matrices and Matlab Applications

Abstract

In this study, firstly, it was shown that the set of real quaternion matrices   MH n is a 4dimensional module over the real matrix ring   M n and 2-dimensional module over the complex matrix ring   M n. Moreover, some new properties of the real quaternion matrices were described. Then, matrix representations of the real quaternion matrices were found easily by Matlab. These matrices were also applied to find the inverse of the real quaternion matrices and inverse matrices were obtained easily with these matrices. In addition, some new properties for matrix representations of the real quaternion matrices were found. Also, the inverse of the 22  real quaternion block matrices was obtained by new methods. Finally, a new method to calculate the determinant of the 22  real quaternion matrices was found and the determinant of these matrices was calculated easily with Matlab application.