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Row & Column Vectors, Dot & Outer Products, Revisited

• To: mathgroup@smc.vnet.net
• Subject: [mg10432] Row & Column Vectors, Dot & Outer Products, Revisited
• From: siegman@ee.stanford.edu (AES)
• Date: Tue, 13 Jan 1998 02:07:31 -0500
• Organization: Stanford University

One of the recent Mathetmatica 3.0 books (sorry, don't have it at hand,
so can't credit it properly), points out that if you define row vectors
in the form

      rowVector={{a1,a2,a3}}; 
      rowVector//MatrixForm

and column vectors in the form

      columnVector={{b1},{b2},{b3}};
      columnVector//MatrixForm

(note the extra curly brackets in both cases), then both the dot
product, namely,

      dotProduct = rowVector . columnVector;
      dotProduct//MatrixForm

and the outer product, e.g.,

      outerProduct = columnVector . rowVector;
      outerProduct//MatrixForm

will work exactly as you expect them to.  Can't say how far this can be
extended into more complex tensor situations, however -- or how much
trouble you'll run into getting rid of the extra brackets in subsequent
calculations.