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If inner products ($V$) are generalisations of dot products ($ \mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($ \mathbb{R}^3$) in some way?

A quick search reveals that they are, but yet the outer product of two column vectors in $ \mathbb{R}^3$ is a 3x3 matrix, not another column vector. What's the link? Thanks!

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    Just found this, on the ambiguity of the term "outer product": http://en.wikipedia.org/wiki/Talk%3AOuter_product#Outer_product_vs_exterior_product2012-08-13

2 Answers 2

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Cross product is much more related to exterior product which is in fact a far going generalization.

Outer product is a matricial description of tensor product of two vectors.

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    Thanks Norbert. Is this map fair? http://math.stackexchange.com/q/182024/218132012-08-13
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The inner product creates a scalar and the outer a skew-symmetric matrix. If you sum like-terms of this matrix you get a vector which also results from the cross product computation.

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    What do you mean by `sum like-terms of this matrix`? How to sum?2016-06-09