This question is about differentiation in $\mathbb{R}^3$.
Let $V : \mathbb{R}^3 \to \mathbb{R}$ be a smooth enough function, $f:\mathbb{R}^3\to\mathbb{R}^3$ its gradient, and $M$ a $3\times 3$ real matrix.
Does there exist a function $W : \mathbb{R}^3 \to \mathbb{R}$ , whose gradient is $Mf$? What would be an expression of $W$?
Thanks!