Re: Non Commutative Multiply

• To: mathgroup at smc.vnet.net
• Subject: [mg128614] Re: Non Commutative Multiply
• From: daniel.lichtblau0 at gmail.com
• Date: Thu, 8 Nov 2012 19:04:11 -0500 (EST)
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```On Thursday, November 8, 2012 1:16:35 AM UTC-6, digo wrote:
> Dear group,
>
>
>
> I want to multiply two matrices, for example,
>
>
>
> A = {{e, f}, {g, h}}
>
> B = {{a, b}, {c, d}}
>
>
>
> Using A.B, Mathematica returns
>
>
>
> {{a e + b g, a f + b h}, {c e + d g, c f + d h}}
>
>
>
> I would like to get, however, the following result:
>
>
>
> {{e a + f c, e b + f d}, {g a + h c, g b + h d}}
>
>
>
> since, for me, the entries {a,b,c,d,e,f,g,h} are operators, i.e., they
>
> are non-commutative.
>
>
>
> I could solve this problem clearing the attribute "Orderless" in the
>
> built-in function Times:
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>
>
> ClearAttributes[Times, Orderless]
>
>
>
> I know, however, this can be dangerous. I tried to define a function
>
> Times2[a_,b_]:=Times[a,b]
>
> and then use ClearAttributes[Times2, Orderless] but it doesn't work.
>
>
>
> How could I solve this problem?
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>
>
>
>
>
> Rodrigo

Could use NonCommutativeMultiply inside Inner.

In[430]:= aA = {{e, f}, {g, h}};
bB = {{a, b}, {c, d}};

In[434]:= Inner[NonCommutativeMultiply, aA, bB, Plus]

Out[434]= {{e ** a + f ** c, e ** b + f ** d}, {g ** a + h ** c,
g ** b + h ** d}}

Daniel Lichtblau
Wolfram Research

```

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