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.