# Explicit form of elements of tensor products

Let $$V$$ and $$W$$ be two vector spaces over $$\mathbb{F}$$. We know that their tensor product $$V \otimes W$$ is also a vector space over $$\mathbb{F}$$. I am wondering how would look like the elements inside it? I.e. if I take a vector $$v \in V$$ and $$w \in W$$, does $$v \otimes w$$ behave as the Kronecker product of $$v$$ and $$w$$?

If I take for example $$\mathbb{C}\otimes_{\mathbb{R}} \mathbb{R}$$ for example, what is the explicit form of its elements?