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A kind of multi-linear multiplication that maps two vectors into a bivector, and combines more complicated tensors in a similar way. The resulting bivector represents the oriented parallelogram defined by the two vectors: imagine the two vectors as adjacent sides of the parallelogram, and take the orientation from the order in which the vectors are presented and the right-hand rule. In 3-space, each bivector can be mapped to a unique vector called the "cross product" (representing a vector normal to the parallelogram and with a length equal to its area—see the unit problem?), so people mostly don't talk about them directly. You start to have problems when you try to understand the effect on the cross product of transforming one of the vectors you're multiplying.

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