三维几何空间中向量叉积的极分解表示  

Expressing the cross product by using polar decomposition in 3-space

作　　者：邓勇[1] 

机构地区：[1]喀什师范学院数学系,新疆喀什844006

出　　处：《黄冈师范学院学报》2014年第6期6-8,共3页Journal of Huanggang Normal University

摘　　要：在三维几何空间中,两个向量a和b的叉积可以由乘积Sab给出,其中Sa是一个仅依赖于a的反对称矩阵,在此基础上,研究了向量叉积与矩阵极分解的内在关系,证明了a和b的叉积是反对称矩阵Sa极分解的一个自然结果,且其极分解是唯一的,最后,利用Rodriguez旋转公式给出了定理1的一个极具说服力的几何解释。The cross product of two vectors a and b in 3-space can be given as a product Sab, where Sa is a matrix that depends only on a. On this basis, we explored the relationship between vector cross product and matrix polar decomposition; moreover showed that this result is a natural consequence of the ＂polar decomposition＂ of the matrix Sa, and the polar decomposition is unique. Finally, a persuasive geometric interpretation of Theorem 1 was given by using Rodriguez rotation formula.

关 键 词：向量 叉积 正交矩阵 半正定矩阵 极分解 

分 类 号：O151.2[理学—数学]