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.
>

```

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