Question

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?

Answer 1

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?

Answer 2

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