Re: Norm, Normalize and column vectors

*To*: mathgroup at smc.vnet.net*Subject*: [mg126397] Re: Norm, Normalize and column vectors*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sun, 6 May 2012 20:30:59 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

On 5/6/12 at 3:24 AM, brenttnewman at gmail.com (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? Mathematica has no concept of row/column vectors. A vector in Mathematica is a 1-d list. That is: In[1]:= a = Range[3]; {VectorQ[a], MatrixQ[a]} Out[2]= {True,False} In[3]:= {VectorQ[{a}], MatrixQ[{a}]} Out[3]= {False,True} In[4]:= {VectorQ[List /@ a], MatrixQ[List /@ a]} Out[4]= {False,True} The documentation specifically states Normalize works with vectors, not matrices. Norm works with matrices. What you a row/column vector is a matrix in Mathematica.