I'm reading a paper describing transformation of gradient of a vector $\mathbf u$ (velocity vector) when I came across the following: $\nabla \mathbf u = \mathbf q$ after transformation is, $$ \nabla_x \cdot (\mathbf u \otimes j \mathbf G^{-1}) = j\mathbf{q} $$ where, $u \in \mathbb R^3$, $\mathbf G$ is a $3\times 3$ matrix, j is a scalar (here, determinant of matrix $G$), $\mathbf q$ tensor or matrix (auxiliary variable role).
How do I go about expanding the tensor product?