Re: Product command with matrices

*To*: mathgroup at smc.vnet.net*Subject*: [mg87861] Re: Product command with matrices*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Fri, 18 Apr 2008 07:13:23 -0400 (EDT)*Organization*: Uni Leipzig*References*: <fu9ft7$ce2$1@smc.vnet.net>*Reply-to*: kuska at informatik.uni-leipzig.de

Hi, Times[] is not Dot[] and Product[] and no equivalent to use Dot[] instedad of Times[] and there is no (easy) way to tell Mathematica that f[1] is a matrix and what may be A a scalar ? a vector or a matrix too ? Even I can't find it out and Mathematica can't know it. You mean DotProduct[mtx_, {i_, i1_, in_}] := Dot @@ Table[mtx, {i, i1, in}] Phi[0] := Id; Phi[n_] := DotProduct[Id + f[i] ** A, {i, 0, n - 1}] and Phi[3] gives (Id + f[0] ** A).(Id + f[1] ** A).(Id + f[2] ** A) Regards Jens J Davis wrote: > I want to define a matrix valued function such as the following (in > LaTeX lingo): > > $$ > X(0)=Id, > X(n)=\prod_{i=0}^{n-1} (Id + f[i] A) > $$ > > where A and f have already been defined and Id is the identity matrix > of appropriate size. > > I tried the following: > > Id=IdentityMatrix[2]; > Phi[0]:=Id; > Phi[n_]:= Product[Id + f[i] A,{i,0,n-1}] > > However, Phi[3] and (Id+f[2]A).(Id+f[1]A).(Id+f[0]A) do not agree. > > Any help around this would be appreciated. >