Let $V$ be a finite-dimensional vector space, let $\omega$ be an alternating covariant $k$-tensor on $V$, and let $\eta$ be an alternating covariant $l$-tensor on $V$. Then$$\omega\wedge\eta=\frac{\left(k+l\right)!}{k!l!}\text{Alt}\left(\omega\otimes\eta\right).$$What is the geometric interpretation of the wedge product?

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across · Answer

I am learning about wedge products to be able to integrate on manifolds. Is it then safe to assume that they are sort of infinitesimals?

amtran_bus · Answer

@ganeshie8 @jim_thompson5910 @uri @thomaster 
These will be able to help you.