MathGroup Archive 2006

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Norm

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68012] Re: [mg67973] Norm
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Thu, 20 Jul 2006 06:04:53 -0400 (EDT)
  • References: <200607190921.FAA21393@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

On 19 Jul 2006, at 11:21, 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
>

Norm[{{0., 1.}, {5., 1.}}, 2]

does not compute the distance between the points {0,1} and {5,1} but  
the 2-norm of the matrix {{0., 1.}, {5., 1.}}. This is defined as the  
square root of the sum of the squares of the matrix entries, in other  
words it is


Sqrt[0^2+1^2+5^2+1^2]//N


5.19615

This is of course completely different form the distance, which is:


Norm[{{0, 1}-{5, 1}}, 2]

5

where - is not the dash but the subtraction sign!

Andrzej Kozlowski


  • References:
    • Norm
      • From: Clausenator@gmail.com
  • Prev by Date: Re: Norm
  • Next by Date: Re: delayed rule evaluation order
  • Previous by thread: Re: Norm
  • Next by thread: Re: Norm