On the Fundamental Spinor Matrices of Real Quaternions

Abstract

In this study, the real quaternions and spinors are studied. The motivation of this study is to express the Hamilton matrices of real quaternions more shortly and elegantly, namely spinors. Therefore, firstly, two transformations between real quaternions and spinors are defined. These transformations are defined for two different spinor matrices corresponding to the left and right Hamilton matrices since the quaternion product is not commutative. Thus, the fundamental spinor matrix corresponding to the fundamental matrix of real quaternions is obtained and some properties are given for these spinor matrices. Finally, the eigenvalues and eigenvectors of the fundamental spinor matrix are obtained.