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

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

Thanks Jackson, for setting up this blog.

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*Related*

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”.