In index notation, does the term $σ_{ik}x_{j}n_{k}$ mean $\bf{σx}\cdot\bf{n}$ or $\bf{xσ}\cdot\bf{n}$? Here $σ$ is a second-order tensor and $x,n$ are vectors.
On the same note, is $$\frac{\partialσ_{ik}}{\partial x_{k}}x_{j}$$ equivalent to $\nabla(\bf{xσ})$ or $\nabla(\bf{σx})$? For some reason there is an index notation rule that eludes me.
Pardon me for the fundamendality or even stupidity of my questions! Long time lurker, first time poster.
In index notation (where summation over a repeated index is implied), matrix-vector multiplication looks like $\left[\mathbf A \mathbf x\right]_i = A_{ij}x_j$, while the dot product looks like $\mathbf x \boldsymbol \cdot \mathbf y = x_iy_i$. Thus, \begin{align*} \sigma_{ik}x_j n_k =\left[\boldsymbol\sigma \mathbf n\right]_ix_j. \end{align*} If, as one of the comments suggests, the current expression has a typo, then the desired result is \begin{align*} \sigma_{ik}x_i n_k &= \left[\boldsymbol \sigma \mathbf n\right]_i x_i\\ &= (\boldsymbol \sigma \mathbf n)\boldsymbol \cdot \mathbf x. \end{align*}