Let $M$ be a $m \times n$ matrix, $x$ a $n$-vector, $y$ a $m$-vector, and $\|\cdot\|_2$ represent the $L_2$ norm (i.e., Euclidean norm). Given $M,y$, the goal is to find $x$ that minimizes the expression
$$\Psi(x) = \|x\|^2 + \|Mx-y\|^2.$$
Is there a closed-form expression for the optimal $x$? Without the $\|x\|^2$ term, this would be an instance of ordinary least squares linear regression and there would be a nice solution, but I'm not sure happens with this additional term.