Let's say a rank 2 tensor $\textbf{T}$ with components $T_{ij}$.
I want to take the divergence of this tensor $\nabla \cdot \textbf{T}$. How would one go about doing this?
Let's say we take the inner product of this tensor with a vector $\textbf{v}$ with components $v_{i}$, in other words $\textbf{v} \cdot\textbf{T}$. This would have components $v_i T_{ij}$ (I think).
How would one take the divergence of this? ie $\nabla \cdot (\textbf{v} \cdot \textbf{T})$?
Thank you