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MathGroup Archive 2003

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Rows & Columns; What do *You* Call a Vector

  • To: mathgroup at smc.vnet.net
  • Subject: [mg43924] Rows & Columns; What do *You* Call a Vector
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Sun, 12 Oct 2003 04:03:44 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

When I create a column vector explicitly using the Mathematica 2D input
method, the result is (assume '(' and ')' are hight-adjusted), 
  
   c1
c=(c2)-> {{c1},{c2},{c3}}.
   c3 

If I create a list of length 3 and apply MatrixForm, the result is

v={v1,v2,v3};

                v1
MatrixForm[v]->(v2).
                v3 

It appears that in matrix multiplication involving traditional (euclidian)
matrix operations, /v/ above behaves as a a row vector when prefixed, and a
column vector when postfixed.  /c/ above is clearly distinct in form from 
v/ above.  How do others approach this situation?  Do you simply work with
'raw' lists, and avoid using the 2D input methods?  Is there a convention
for using the 'vectors' produced by the 2D input methods, such as
List[List[r1,r2,r3]]<=>row vector, and
List[List[c1],List[c2],List[c3]]<=>column vector?

The reason I ask is because when I first began using Mathematica, I
attempted to use the 2D input vectors, and found the results to be
different than expected.  I've also noticed that /mmf = MatrixForm[m]/
tends to behave differently from /m/ in some cases.  Unless there is some
underlying unifying principle, and/or, convention that makes these various
forms interoperate, it seems the 2D input methods for creating vectors
should be avoided except where they are for purly textual purposes, i.e.,
they should not be used for doing math. 

-- 
Gelonus, Kucha, Kizil, Sampul, Dunhuang, Kanishka, Cherchan, Margiana,
Sintashta, Himmelsscheibe von Nebra, Ryazan Russia,  Afanasevo, Peñon
Woman, Guancha, Maes Howe, Purushkhanda.


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