# How does one take the Divergence of a Tensor?

I’m trying to understand the derivation of the Maxwell stress tensor in Heald and Marion. Im confused how they go from 4.101 to 4.102 in the image above. I can't seem to see how 4.101 is the divergence of the tensor described in 4.102. I think my misunderstanding might stem from the fact that I'm not sure how to take the divergence of a tensor. Can someone explain how this is done / how one goes between the two equations in the image?

In index notation, the divergence of a vector is $$\partial_iA_i$$ and by analogy the divergence of a tensor with two indices means either $$\partial_iA_{ij}$$ or $$\partial_jA_{ij}$$. In the case of a symmetric tensor, these are the same thing.
When working with Cartesian components in 3D space, you can keep all indices lowered (or raised). A repeated (“contracted”) index implies a sum over the index values 1, 2, 3 for $$x, y, z$$.
With this information, you should be able to take the divergence of $$T_{ij}$$. To compare it with 4.101, express 4.101 in index notation as well. If you don’t understand double cross products in index notation, make that a separate question.