1. ## Vectors notation

What do double bars around a vectors name indicate? For example they are used at the Triangle inequality page of wikipedia. I am struggling to understand a proof written elsewhere.

2. Originally Posted by Stuck Man
What do double bars around a vectors name indicate? For example they are used at the Triangle inequality page of wikipedia. I am struggling to understand a proof written elsewhere.
$\displaystyle ||\bar{v}||$ indicates the magnitude, or "norm" , of a vector ... i.e. its length.

3. Is it an alternative notation to single bars?

4. Originally Posted by Stuck Man
Is it an alternative notation to single bars?
actually, the single bar notation is the alternative.

5. I wonder why does the page I mentioned confuse things by using both notations in the same section?

6. Originally Posted by Stuck Man
I wonder why does the page I mentioned confuse things by using both notations in the same section?
If $\displaystyle \alpha$ is a scalar and $\displaystyle \vec{v}$ vector then $\displaystyle \left\| {\alpha \vec{v}} \right\| = \left| \alpha \right|\left\| \vec{v} \right\|$
Is that what you mean by using ‘both’ notations on the same page?
If so those are not the same. One is the absolute value of a scalar(a number) the other is length of a vector.
As was said, some authors use only the single bar for both concepts.

7. Also one possibility, which I doubt is the case, but is entirely possible, consider a vector of one dimension $\displaystyle V = <-2>$ and the scalar $\displaystyle -2$, the following is true:
$\displaystyle ||V||=|-2|$. This is so because $\displaystyle ||V||=\sqrt{(-2)^2} = \sqrt{4} = 2$ and $\displaystyle |-2| = 2$. So, in a strange abuse of notation, the absolute value of the componant of a one dimensional vector is equal to its magnitude. Now, I doubt that wikipedia would use such a rare case, and such an "abusive of notation" to denote this fact. I'm sure its highly more likely that its simply the alternative notation for the magnitude of a vector. But its interesting to see a relationship between the two notations based on the fact that:

$\displaystyle |a| = \sqrt{a^2}$

Thats my two cents, take it for what its worth.