# An easy exercise

This is a simple question to test your understanding of tensor products, if you wish. If $U$ and $V$ are vector spaces over some field of dimension $n$ and $m$ respectively, then $U \otimes V$ has dimension $nm$. Vector spaces of equal dimension are automatically isomorphic, so why don’t we just define $U \otimes V$ to be the ‘unique’ vector space of dimension $nm$?

If the contents of my talk made sense to you, the answer should be obvious.

Thanks Jackson, for setting up this blog.