Comment by seanhunter

There are lots of people who write math in a way that is very easy for others (of an appropriate level of experience let’s say) to understand. I also didn’t find this particularly hard to follow, although some of it is I think a little fast and loose. eg

   > In general, given two finite-dimensional vector spaces U and W, then U ≃ W exactly when dim(U)=dim(W).

Is that really true? I don’t think it is. Specifically surely at least they have to be vector spaces either over the same field or over fields which are themselves isomorphic. I’m thinking say U is a vector space over R and W is a vector space over Q. Dim(U) = Dim(W)=1 but U and W are not isomorphic because there exists no bijection between the reals and the rationals.