If one column contains the basis vectors of one space, and another column contains the basis vectors of another space, then their cross join will contain all pa

If one column contains the basis vectors of one space, and another column contains the basis vectors of another space, then their cross join will contain all pairs of basis vectors. If you were to take the tensor product of each pair you'd end up with a basis for the tensor product space. This is because the Cartesian product shows up in both places. I'm not sure if this is what the parent comment is getting at, and I'm not sure I see anything deep lurking there, but that could just be me.