# How to understand the two vertical lines ||

• Jun 30th 2010, 03:00 AM
dervast
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
• Jun 30th 2010, 03:07 AM
Zaph
That would be the 'length'
• Jun 30th 2010, 03:51 AM
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.
• Jun 30th 2010, 05:20 AM
dervast
Quote:

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.

So it is enough to say that it refers to the Euclidean distance. I am still wondering why some texts wants to make life that hard when there are always simple ways to express things.
Best Regards
Alex
• Jun 30th 2010, 06:01 AM
HallsofIvy
What is so "hard" about that notation?

What level text was this? There is usually a list of symbols, either in the very front or very back of the text book for an introductory text. In a more advanced text, of course, you would be expected to already know standard notation.