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Re: Norm, Normalize and column vectors

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  • Subject: [mg126394] Re: Norm, Normalize and column vectors
  • From: Murray Eisenberg <murray at>
  • Date: Sun, 6 May 2012 20:29:57 -0400 (EDT)
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  • Reply-to: murray at

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
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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