advanced_tools:exterior_product
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advanced_tools:exterior_product [2023/03/19 21:33] edi [Concrete] |
advanced_tools:exterior_product [2025/03/04 00:51] (current) edi [Concrete] |
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| The exterior product of two 3D vectors is a rank-2 tensor with three independent components (shown in red), which match those of the cross product. The exterior product of three 3D vectors is a rank-3 tensor with only one independent component (shown in red), which matches the (scalar) triple product. The exterior product of a 3D vector and an antisymmetric tensor is again a rank-3 tensor with only one independent component (shown in red), which is related to the scalar product. | The exterior product of two 3D vectors is a rank-2 tensor with three independent components (shown in red), which match those of the cross product. The exterior product of three 3D vectors is a rank-3 tensor with only one independent component (shown in red), which matches the (scalar) triple product. The exterior product of a 3D vector and an antisymmetric tensor is again a rank-3 tensor with only one independent component (shown in red), which is related to the scalar product. | ||
| - | For a more detailed explanation of this picture see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#exterior_prod|Fun with Symmetry]]. | + | For a more detailed explanation of this picture see [[https://esackinger.wordpress.com/appendices/#exterior_and_clifford_products|Fun with Symmetry]]. |
| [{{ :advanced_tools:exterior_prod.jpg?nolink }}] | [{{ :advanced_tools:exterior_prod.jpg?nolink }}] | ||
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