I have a vector field $\vec{F}$, which at every point in space is multiplied by some values given by a matrix A: i.e., $\left[A\right]\vec{F}$. I then want to compute a closed loop integral around some points in this space on a curve $C$:
$$ \oint_C \left(\left[A\right]\vec{F} \right)\cdot d\vec{C} $$
If the matrix A is position-invariant, am I able to remove it from the integral? i.e.:
$$ \oint_C \left(\left[A\right]\vec{F} \right)\cdot d\vec{C} \stackrel{?}{~=~} \left[A\right] \oint_C \vec{F} \cdot d\vec{C} $$
The integral on the left evaluates to a number, while the right hand side is a matrix times a number, so they aren't even the same type of thing.