摘要
探讨了3维欧氏空间的向量积在高维空间推广的可能性.在三条假设下推导出高维空间中的向量积所应具备的若干性质,证明了在某些意义下向量积仅存在于R3,并举例说明R7与R3中向量积不同的根源.
The possibility of the vector product in multi-dimensional space was discussed. Several properties that the vector product in multi-dimensional space should have was proved under three essential hypotheses. Then the vector product can merely exist in R^3 was concluded. The source that casuses the difference on the vector products between R^ 7 and R^ 3 was showed.
出处
《大学数学》
2014年第3期74-78,共5页
College Mathematics
基金
上海高校选拔培养优秀青年教师科研专项基金(SSC09024)
上海海洋大学博士科研启动金
关键词
欧氏空间
向量积
三重矢积
维数
Euclidean space
vector product
triple vector product
dimension
