# Divergence of a rank-2 tensor in Einstien summation

1. Dec 29, 2013

### Niles

1. The problem statement, all variables and given/known data
Hi

When I want to take the divergence of a rank-2 tensor (matrix), then I have to apply the divergence operator to each column. In other words, I get
$$\nabla \cdot M = (d_x M_{xx} + d_y M_{yx} + d_zM_{zx}\,\, ,\,\, d_x M_{xy} + d_y M_{yy} + d_zM_{zy}\,\,,\,\, d_x M_{xz} + d_y M_{yz} + d_zM_{zz})$$
How would I write this vector in Einstein summation? Is it correct that it would be
$$\partial_i M_{ij}$$

2. Dec 29, 2013

### 1MileCrash

IIRC, yes.

You have three entries, that distinguished by a new j value, since it appears once, and each entry is a summation over i, since it appears twice.