       Re: Deformed Matrix Product

• To: mathgroup at smc.vnet.net
• Subject: [mg72191] Re: Deformed Matrix Product
• From: dh <dh at metrohm.ch>
• Date: Thu, 14 Dec 2006 05:49:06 -0500 (EST)
• References: <eloom4\$mu6\$1@smc.vnet.net>

```
Hi Simone,

let's first define a member function that specifies if a term is to be

included in the sum or not:

memQ[i_,j_,k_]:=If[i<=k

,If[i\[LessEqual]j\[LessEqual]k,1,0]

,If[j\[LessEqual]k||i\[LessEqual]j,1,0]

]

With this we do the "inner product" by hand (assuming that the factors

have dimension: n x n):

DeformedProduct[a_,b_]:=(n=Length[a];Table[Sum[a[[i,j]] memQ[i,j,k]

b[[j,k]] ,{j,n}],{i,n},{k,n}]))

We can test this by defining two 4x4 matrices:

ma = Array[a, {n, n}]; mb = Array[b, {n, n}];

and get the product:

DeformedProduct[a,b]//TableForm

Daniel

simoseve at gmail.com wrote:

> Dear All,

>

> I would like to implement a form of matrix product called deformed

> matrix product.

>

> The definition can be found at page 2 of

>

> http://ipnweb.in2p3.fr/lptms/membres/pzinn/semi/ium.pdf

>

> P. Zinn-Justin, Combinatorics of the Brauer Loop scheme.

>

> Is there any good samaritan out there that knows how to do it?

>

> Thanks a lot for your time and kind consideration.

>

> Simone Severini

>

```

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