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>*Reply-to*: murray at math.umass.edu

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

**References**:**Norm, Normalize and column vectors***From:*Brentt <brenttnewman@gmail.com>