R^7中一个叉积性质的初等证明(英文)  

An elementary proof for a property of cross product in R^7

作　　者：王晋勋[1] 李兴民[1] 

机构地区：[1]华南师范大学数学科学学院,广东广州510631

出　　处：《广州大学学报（自然科学版）》2008年第3期30-32,共3页Journal of Guangzhou University:Natural Science Edition

摘　　要：彭立中教授等人定义了七维空间中两个向量的叉积,并证明了两个七维向量平行当且仅当它们的叉积为零.然而,其证明是借助于计算机完成的.文章利用Cauchy-Schwarz不等式及八元数的一些性质,给出了它的一个初等证明.Prof PENG Li-zhong,et al. had defined the cross product of two vectors in 7-dimensional space, and had proved that any two 7-dimensional vectors are parallel if and only if their cross product equals zero. However, their proof makes use of computer programs. By using the Cauehy-Sehwarz inequality and the properties of oetonions, we give an elementary proof of it.

关 键 词：八元数 R^7中的叉积 Cauchy—Schwarz不等式 

分 类 号：O151[理学—数学]