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?