7 replies to this topic

[fireside]

I was looking at a formula and it had two lines on each side of a variable like
|| a ||

I know one on each side is absolute value, what is it when two are used?

[Reedbeta]

Usually that means the length of a vector, or more generally in mathematics, a "norm" (generalization of the concept of vector length).

Some people use single bars for vector lengths as well, but some prefer to use two to distinguish scalars from vectors.

[fireside]

OK, so it would be a normalized vector then? I think that's what I was reading about.

[Reedbeta]

Usually ||x|| is just the length of x. If you saw x / ||x|| that would be normalize(x).

Some people also use a caret over a vector to mean normalization, like û would be normalize(u). Other kinds of decorations can be used too; there's not really a standard.

[fireside]

Yeah, that's what it was. I also saw the caret. That clears the whole thing up then, thanks.

[.oisyn]

Reedbeta, on 11 January 2012 - 10:56 PM, said:

Some people use single bars for vector lengths as well, but some prefer to use two to distinguish scalars from vectors.

Or to distinguish between vector norm and set cardinality.

[TheNut]

I think in the mathematics world it is formally called magnitude. At least that's what I remember from my algebra days. Otherwise, all of the above = good.

[}:+()___ (Smile)]

Usually norm have definition in the beginning of mathematical article, as there are many kind of norms (see wikipedia):
||x||₁ = sum |x_i|,
||x||₂ = sqrt(sum x_i²),
||x||_ꝏ = max |x_i|.