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?

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

Euclidean norm ($L^2$ norm); see this Wikipedia article – J. W. Tanner May 30 '19 at 00:09 — J. W. Tanner, May 30 '19 at 00:09
ah, I see. Thank you. – Timothy Pulliam May 30 '19 at 00:15 — Timothy Pulliam, May 30 '19 at 00:15

score 2 · Accepted Answer · answered May 30 '19 at 00:18

2

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 $||x||_1$.

answered May 30 '19 at 00:18

J. W. Tanner

1 Answers1