*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.