# What do double vertical lines mean?

I am reading a paper on computer graphic and having hard time to understand this formula:

1. What is the double vertical lines means? Do they always go with power of 2?
2. If I want to learn further about this equation, which subset of math should I look into?
• Without the $^2$, it means the distance between the first term and the second. But they are considering the square of the distance, largely because squares of distances are better behaved than distances. – André Nicolas Aug 27 '14 at 5:54
• In addition, you don't really need to look at a particular area of math to learn about this equation. You probably just need to know how to calculate the distances between two points and perhaps the triangle inequality. – fixedp Aug 27 '14 at 5:56
• When do people normally use the double vertical line? What is it called mathematically? – sooon Aug 27 '14 at 5:59
• The word you a are looking for is "norm" or "normed space". wikipedia might help on this topic. Alternatively, in the case of finite dimensions any book/script on linear algebra should do it. – Quickbeam2k1 Aug 27 '14 at 6:01
• I found these series of videos that explained this from KhanAcademy. – sooon Aug 27 '14 at 7:15