关于四元数体上矩阵对角化的几个定理

摘要

近年来矩阵对角化理论研究得到了充分的发展，并且在分析方法、研究领域、研究的深度和广度上都有了突破。但在四元数体上，由于四元数乘法的非交换性，人们对四元数体上矩阵对角化的研究甚少。对四元数体上矩阵对角化进行研究，得到了几个重要结论。%　　In the recent years, matrix diagonalization theoretical research has been fully developed, and has achieved a breakthrough in the analysis methods, research areas, the depth and breadth of research. But on the Quaternion body, the quaternion multiplication is non-exchangeable, and there has been little study of matrix di⁃agonalization on the quaternion. In this paper, some study is made of the quaternion matrix diagonalization, and several important conclusions are reached.