Re: Non Commutative Multiply

• To: mathgroup at smc.vnet.net
• Subject: [mg128613] Re: Non Commutative Multiply
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Thu, 8 Nov 2012 19:03:51 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
• Delivered-to: mathgroup-newsend@smc.vnet.net
• References: <20121108070906.3772668D2@smc.vnet.net>

```Use Inner

A = {{e, f}, {g, h}};
B = {{a, b}, {c, d}};

Inner[NonCommutativeMultiply, A, B]

{{e ** a + f ** c, e ** b + f ** d}, {g ** a + h ** c, g ** b + h ** d}}

(% /. NonCommutativeMultiply -> Times) == A.B

True

Bob Hanlon

On Thu, Nov 8, 2012 at 2:09 AM, Rodrigo AP <digorna at gmail.com> 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:
>
> 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?
>