This might be a simple question but I just cannot formualte a general formula.
Say I define a set:
$$S = \{x:Ax=b\}$$ where $A$ is full rank. Then what will be the projection of any general point $y$ on this set $S$ i.e find $x^*$ such that $Ax^*=b$ and distance between $x^*$ and $y$ is minimum.