# Thread: How to understand the two vertical lines ||

1. ## How to understand the two vertical lines ||

Hello I read the following equation
Imageshack - log.gif
but I do not understand what the
|| (what ever is inside) ||2 (with the 2 as a small number -- called index?)

Best Regards
Alex

2. That would be the 'length'

3. $|| \mathbf{a} ||$ is a notation that represents the "length" of a vector $\mathbf{a}$. In your expression, $\mathbf{x} - \mathbf{x}_r$ is the vector whose length is being calculated.

Since "length" can be defined in a number of ways, the subscript $2$ indicates that the length is calculated using the Euclidean norm. So, $||\mathbf{x} - \mathbf{x}_r||_2$ means that you should find the length of the vector $\mathbf{x} - \mathbf{x}_r$ as defined by the Euclidean norm.

The Euclidean norm is the most intuitive definition of length. For example, if you have a vector $(4,-3)$, its Euclidean length would be $5$. You can conceptualize this as the distance between the point $(4,-3)$ and the origin.

4. Originally Posted by drumist
$|| \mathbf{a} ||$ is a notation that represents the "length" of a vector $\mathbf{a}$. In your expression, $\mathbf{x} - \mathbf{x}_r$ is the vector whose length is being calculated.

Since "length" can be defined in a number of ways, the subscript $2$ indicates that the length is calculated using the Euclidean norm. So, $||\mathbf{x} - \mathbf{x}_r||_2$ means that you should find the length of the vector $\mathbf{x} - \mathbf{x}_r$ as defined by the Euclidean norm.

The Euclidean norm is the most intuitive definition of length. For example, if you have a vector $(4,-3)$, its Euclidean length would be $5$. You can conceptualize this as the distance between the point $(4,-3)$ and the origin.