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

```

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