【摘要】 在超复数系下，重点研究狄拉克矩阵的导出以及其固有的关联性，通过计算机来进行数值验证.先从超复数中的四元数定义出发，结合实虚矩阵的表达方式，给出一种获取狄拉克矩阵的广义表示方法.基于对四元数情况下的狄拉克矩阵进行重点研究分析，给出一组实矩阵与超复数系的对应关系，探索性地对超复数系中的其他情形给予定性研究.通过二元数、八元数以及十六元数等情形的计算实例，进一步验证狄拉克矩阵在超复数系下关联性的可行性和准确性.更多还原

【Abstract】 In the field of hyper-complex numbers, this article focused on the derivation of Dirac matrices and their inherent relevances, which were numerically validated through computers. This article started with the definition of quaternions in hyper-complex numbers and combined the representation of real and imaginary matrices to provide a generalized method for obtaining Dirac matrices. Afterwards, we focused on researching and analyzing the Dirac matrix in the case of quaternions, provided a set of correspondence between real matrices and hyper-complex systems, and explored qualitative research steps for other situations in the field of hyper-complex numbers. We further validated the feasibility and accuracy of studying the relevances of Dirac matrices in the field of hyper-complex numbers through computational examples of double-element numbers, octonion, and sedenion.更多还原