Re: Product command with matrices
- To: mathgroup at smc.vnet.net
- Subject: [mg87864] Re: [mg87834] Product command with matrices
- From: Sseziwa Mukasa <mukasa at jeol.com>
- Date: Sat, 19 Apr 2008 03:31:57 -0400 (EDT)
- References: <200804180640.CAA12618@smc.vnet.net>
On Apr 18, 2008, at 2:40 AM, 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 You are confusing Dot and Product, do you want to multiply matrix elements together eg: {{a,b},{c,d}} {{e,f},{g,h}} = {{a e,b f},{c g,d h}} or do a regular matrix multiply? If the latter then Phi[n_]:=Fold[(Id+#2 A).#1&,Id+f[0] A,Table[f[i],{i,1,n-1}]] should work. Regards, Ssezi
- References:
- Product command with matrices
- From: J Davis <texasAUtiger@gmail.com>
- Product command with matrices