Re: Matrix Multiplication (with a twist)

*To*: mathgroup at smc.vnet.net*Subject*: [mg68989] Re: [mg68951] Matrix Multiplication (with a twist)*From*: "Carl K. Woll" <carlw at wolfram.com>*Date*: Sat, 26 Aug 2006 02:04:25 -0400 (EDT)*References*: <200608250935.FAA09217@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Bruce Colletti wrote: > For matrix A = {{e,f},{g,h}} and B = {{a,b},{c,d}}, Mathematica returns their product > > A.B = {{ae+cf,be+df},{ag+ch,bg+dh}} > > However, I want to treat multiplication of numeric variables as noncommutative in order to instead obtain the result > > {{ea+fc, eb+fd},{ga+hc,gb+hd}} > > How would this be done in v5.2? Thanks. > > Bruce One possibility is to use Inner where NonCommutativeMultiply does the multiplication: In[13]:= Inner[NonCommutativeMultiply, A, B, Plus] Out[13]= {{e ** a + f ** c, e ** b + f ** d}, {g ** a + h ** c, g ** b + h ** d}} I actually prefer using one of the other typesetting symbols with no function definition instead, such as CenterDot: In[14]:= Inner[CenterDot, A, B, Plus] Out[14]= {{eÂ·a + fÂ·c, eÂ·b + fÂ·d}, {gÂ·a + hÂ·c, gÂ·b + hÂ·d}} Carl Woll Wolfram Research

**References**:**Matrix Multiplication (with a twist)***From:*Bruce Colletti <vze269bv@verizon.net>