Re: Re: Norm
- To: mathgroup at smc.vnet.net
- Subject: [mg68058] Re: [mg68004] Re: [mg67973] Norm
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Fri, 21 Jul 2006 05:37:49 -0400 (EDT)
- Organization: Mathematics & Statistics, Univ. of Mass./Amherst
- References: <200607190921.FAA21393@smc.vnet.net> <200607201004.GAA09828@smc.vnet.net>
- Reply-to: murray at math.umass.edu
- Sender: owner-wri-mathgroup at wolfram.com
Correction to my posting: What I mean to write is that the desired
euclidean distance is given by
Norm[{0,1} - {5,1}]
and the result is 5.
Murray Eisenberg wrote:
> Mathematically, the norm of a vector gives that vector's length. And
> the distance between two vectors is the norm of the difference between
> the two vectors. (What you call the "dash" is in fact a subtraction sign.)
>
> So, assuming you want the ordinary (that is, Euclidean) distance, the
> desired result is given by
>
> Norm[{0, 1, 5, 1}]
>
> and the result (in InputForm) is 3 Sqrt[3].
>
> The final argument, 2, is superfluous in the case of the ordinary
> (Euclidean) norm, which is the 2-norm.
>
> It would help when doing such things if you were familiar, first, with
> the underlying mathematical ideas and second, with the documentation
> that Mathematica itself provides. For the latter, just evaluate
>
> ?Norm
>
> and then to get further information click the hyperlink in the output
> produced (or in the first instance look up Norm directly in the
> HelpBrowser).
>
>
>
>
> Clausenator at gmail.com wrote:
>> Hi,
>> I want to calculate a distance matrix, similar to (as poorly explained
>> at) http://en.wikipedia.org/wiki/Distance_matrix
>>
>> I found out about the Function "Norm" in mathematica 5.
>>
>> Here is a little example. I want to calculate the distance between
>> vectors {0,1} and {5,1}. The distance should be 5
>>
>> Now,
>>
>> Norm[{{0., 1.}, {5., 1.}}, 2]
>> results 5.10293
>>
>> Norm[{{0., 1.} - {5., 1.}}, 2]
>> results 5.0
>>
>> According to the documentation I have (Mathematica Help Browser, search
>> for "Norm" under "Built-in Functions") the version with the comma is
>> documented. I like the solution with the dash better.
>> Which one is it? In other words, is there some Wolfram description or
>> can you explain the difference?
>>
>> Thanks for your help,
>> Claus
>>
>>
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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