# 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.

## One thought on “An easy exercise”

1. Thanks Jackson for making the blog, and Stephen for posting the exercise. Note that this exercise is related to exercise 10 below. The key word being “canonical”.