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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