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
where we added TableForm for more readability.
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
>