I am reading a paper where they try to solve some linear system of equations. Using:
$$ y = \min_x \frac{1}{2}||Dx-d||_2^2 $$
Probably a very beginner question, but I am wondering, why is the division by $2$ placed in the front? From what I gather we are trying to minimize the $L^2$ norm of the RSS. The RSS is just the squared differences between $Dx$ and $d$, and the $2$-norm also doesn't involve any division.
The constant factor of $\frac{1}{2}$ doesn't change the location of the minimum, as you observe. The factor is there because $$\frac{d}{d\vec{x}}\left\|D\vec{x} - d\right\|^2 = 2D^T(D\vec{x}-d)$$ and hence the factor of $2$ and $\frac{1}{2}$ cancel, making the expression for the derivative simpler. It's purely by convention.