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According to Wikipedia:

The divergence of a continuously differentiable tensor field $\underline{\underline{\epsilon}}$ is:

$\overrightarrow{\operatorname{div}}\,(\mathbf{\underline{\underline{\epsilon}}}) = \begin{bmatrix} \frac{\partial \epsilon_{xx}}{\partial x} +\frac{\partial \epsilon_{xy}}{\partial y} +\frac{\partial \epsilon_{xz}}{\partial z} \\ \frac{\partial \epsilon_{yx}}{\partial x} +\frac{\partial \epsilon_{yy}}{\partial y} +\frac{\partial \epsilon_{yz}}{\partial z} \\ \frac{\partial \epsilon_{zx}}{\partial x} +\frac{\partial \epsilon_{zy}}{\partial y} +\frac{\partial \epsilon_{zz}}{\partial z} \end{bmatrix} $

How do you get this formula from the definition of divergence? Either formally, or with some abuse of notation?

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    I don't have a high enough reputation to comment, but note that the equation in the original post is not correct: $\epsilon_{ij}$ should be replaced with $\epsilon_{ji}$ in all of the term numerators.2017-08-22

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If S a matrix, with columns $S^{j}$, $j=1$, $n$ then $\mathrm{div}(S)_{j} = \mathrm{div}(S^{j})$.

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    hmmm are you sure? I think this is not (always) right. consider a 3x2 matrix that depends on two variables.2016-09-20