In my finite element method book, there is a notation which is confusing me. Given $v:R^2\rightarrow R^2$, I'm supposed to evaluate
$\sigma\cdot \nabla v^T$
where $\sigma$ is a smooth tensor valued function. What is confusing me is the notation $\nabla v^T$. How do I interpret the gradient of a vector? Is it a matrix or a vector? Also, should I interpret the equation as $\nabla (v^T)$ or $\nabla^T v$?