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arXiv · 1310.5197

Vector cross product in n-dimensional vector space

Xiu-Lao Tian·Chao Yang·Yang Hu·Chao Tian
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Abstract

The definition of vector cross product (VCP) introduced by Eckmann only exists in thethree- and the seven- dimensional vector space. In this paper, according to the orthogonal completeness, magnitude of basis vector cross product and all kinds of combinations of basis vector $\hat{e}_i$, the generalized definition of VCP in the odd n-dimensional vector space is given by introducing a cross term $X_{AB}$. In addition, the definition is validated by reducing the generalization definition to the fundamental three- and seven-dimensional vector space.

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Xiu-Lao Tian, Chao Yang, Yang Hu, Chao Tian. 2013-10-19. Vector cross product in n-dimensional vector space. https://arxiv.org/abs/1310.5197

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