two lines on each side of a variable

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fireside 141 Jan 11, 2012 at 22:27

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?

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Reedbeta 167 Jan 11, 2012 at 22:56

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.

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fireside 141 Jan 11, 2012 at 23:11

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

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Reedbeta 167 Jan 11, 2012 at 23:13

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.

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fireside 141 Jan 11, 2012 at 23:26

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

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_oisyn 101 Jan 11, 2012 at 23:52

@Reedbeta

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.

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TheNut 179 Jan 12, 2012 at 00:26

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.

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__________Smile_ 101 Jan 12, 2012 at 04:19

Usually norm have definition in the beginning of mathematical article, as there are many kind of norms (see wikipedia):
||x||1 = sum |xi|,
||x||2 = sqrt(sum xi2),
||x||ꝏ = max |xi|.