What does the subscript $2$ mean in the expression $\min_{w} || X w - y||_2^2$?

Question

What does the bottom $2$ mean in the following expression?

$$\min_{w} || X w - y||_2^2$$

Answer 1

The Euclidean norm of a vector $\vec x \in \mathbb R^n$ given by $\sqrt{x_1^2+x_2^2+...+x_n^2}$ can be denoted $ ||x||_2$.

This distinguishes it from other norms, such as the "taxicab norm" given by

$|x_1|+|x_2|+...+|x_n|$ and denoted $||x||_1$.