| 三维几何空间中向量叉积的极分解表示 |
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| 引用本文： | 邓勇.三维几何空间中向量叉积的极分解表示[J].黄冈师范学院学报,2014(6):6-8. |
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| 作者姓名： | 邓勇 |
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| 作者单位： | 喀什师范学院 数学系,新疆 喀什,844006 |
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| 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。
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| 关 键 词： | 向量 叉积 正交矩阵 半正定矩阵 极分解 |
Expressing the cross product by using polar decomposition in 3-space |
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| DENG Yong.Expressing the cross product by using polar decomposition in 3-space[J].Journal of Huanggang Normal University,2014(6):6-8. |
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| Authors: | DENG Yong |
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| Institution: | DENG Yong (Department of Mathematics, Kashgar Teachers College, Kashgar 844006, Xinjiang, China) |
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| Abstract: | 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. |
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| Keywords: | vector cross product orthogonal matrix semi-definite matrix polar decomposition |
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