Re: How to mutiply a 3x1 and 1x3 vector

*Subject*: [mg3082] Re: [mg3068] How to mutiply a 3x1 and 1x3 vector*From*: rpratt at math.unc.edu (Robert Pratt)*Date*: 31 Jan 1996 04:39:35 -0600*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.*Sender*: daemon at wri.com

I would suggest two equivalent approaches. In either case, you need to define A and B so that Mathematica recognizes them as matrices (lists of row vectors, which are themselves lists) rather than just lists of elements. Method 1: A={{1, 2, 3}} B={{3, 4, 5}} Note that MatrixQ[A] and MatrixQ[B] return True, but MatrixQ[{1, 2, 3}] and MatrixQ[{3, 4, 5}] return False. Transpose[A]//MatrixForm B//MatrixForm Transpose[A].B//MatrixForm This last command returns a 3x3 matrix, the desired result. Here, the //MatrixForm is just for appearance (so that the output looks like a matrix). You can omit it if you wish. Method 2: A={{1}, {2}, {3}} B={3, 4, 5} A.B//MatrixForm Which method you use depends on your preference. Method 1 is better if you want to define all your vectors in a consistent manner. For example, if you need to compute both A.B and B.A, you would want to define A and B similarly (both as row vectors or both as column vectors). You then have to transpose before multiplying. However, method 2 saves one step in the calculation since you're performing the transpose "manually" in your definition of A. Rob Pratt Department of Mathematics The University of North Carolina at Chapel Hill CB# 3250, 331 Phillips Hall Chapel Hill, NC 27599-3250 rpratt at math.unc.edu On Tue, 30 Jan 1996, Stephen Nichols wrote: > > Hi, > > I have another question that I thought would be simple to to in Mathematica. > I have two vectors A={1,2,3} and B={3,4,5}. How do I multiple them together > to get a 3x3 matrix. A . B gives me a scalar result. Mma seems to always > treat the first one as a row vector and the second as a column vector. I > need it to do the opposite. Treat the first as a column vector and the second > as a row vector. Any ideas? > > thanks, > > >