       Re: Norm, Normalize and column vectors

• To: mathgroup at smc.vnet.net
• Subject: [mg126394] Re: Norm, Normalize and column vectors
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 6 May 2012 20:29:57 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201205060724.DAA02410@smc.vnet.net>

```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:= Norm[{{1}, {2}, {3}}]
>
> Out= Sqrt
>
> But
>
> In:=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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