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Re: Norm, Normalize and column vectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126403] Re: Norm, Normalize and column vectors
  • From: Brentt <brenttnewman at gmail.com>
  • Date: Tue, 8 May 2012 04:08:37 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201205060724.DAA02410@smc.vnet.net>

Thank you. Someone else said it had to do with the fact that the model for
lists in Mathematica is based on tensors (or something). This prompted me
to go look up what tensors are, and since I'm just now finishing up my
first course in Linear Algebra my mind throughly blown. But I still don't
understand it.

Your answer makes sense to me at least. Unexplained, possibly arbitrary
design decisions I can understand---tensors not so much at this point.

On Sun, May 6, 2012 at 5:29 PM, Murray Eisenberg <murray at math.umass.edu>wrote:

> It's impossible to know _why_ without being able to read the minds of
> the developers!
>
> A more proximate reason is the documentation: ref/Norm says Norm[expr]
> "gives the norm of a number, vector, or matrix" whereas ref/Normalize
> says Normalize[v] "gives the normalized form of a vector v".
>
> Whether Normalize ought to be extended to have the same domain as Norm
> -- that's a different question. At first glance, that would seem
> desirable, but then I don't know what the implications of such an
> extension would be for the rest of the system.
>
>
> On 5/6/12 3:24 AM, Brentt wrote:
> > Why does Norm work with column vectors, but Normalize does not?
> >
> > e.g..
> > In[1]:= Norm[{{1}, {2}, {3}}]
> >
> > Out[1]= Sqrt[14]
> >
> > But
> >
> > In[2]:=Normalize[{{1}, {2}, {3}}]
> >
> > Throws red
> >
> >
> > It even says in the documentation that Normalize[v] essentially returns
> >
> > Times[Power[Norm[v],-1],v],   except returning the 0 vector for the 0
> > vector.
> > Strangely, the above "equivalent" expression would handle all but th 0
> > column vector with aplomb.
> >
> > I find this curious. Is there a good explanation for this?
> >
>
> --
> 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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