从四元数到向量:向量概念演变的历史分析

From quaternions to vector:historical analyses of the evolution of the vectorial idea

目的考察和分析从四元数到向量的发展历程。方法运用文献考证和历史分析的方法对向量概念的演变进行研究。结果现代向量系统是从四元数发展而来的,是寻找物理现象的数学表示的结果;通过对哈密顿四元数与格拉斯曼系统的对比分析指出其历史的必然性。结论向量概念的演变主要是为了满足物理学的需要,它揭示了科学变革的一般规律。

Aim To check and analyze the developmental process from quaternions to vector. Methods The methods of historical analysis and textual research are used to study the evolution of the idea of a vectorial system. Results Vector algebra and vector analysis are the production of quaternions and the result of seeking mathematical indication of physical phenomenon, it＇s the historic certainty as well as.the effect of some accidental elements. Conclusion If mathematical discovery is too general or surpasses the mathematical tradition in those years, it＇s difficult to be accepted. The evolution of the idea of a vectorial system gives physics a more reasonable and more powerful mathematic method, revealing the common laws of scientific evolution.