think there's a typo here:

> There's a [tensor product](https://en.wikipedia.org/wiki/Tensor_product#Tensor_product_of_vector_spaces) \\(V \otimes W\\) of vector spaces \\(V\\) and \\(W\\), which has dimension equal to the dimension of \\(\mathcal{V}\\) and the dimension of \\(\mathcal{W}\\).

should read "the dimension of \\(\mathcal{V}\\) **times** the dimension of \\(\mathcal{W}\\)" surely?