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RE: symbolic matrix inverse

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94159] RE: [mg94126] symbolic matrix inverse
  • From: "Jose Luis Gomez" <jose.luis.gomez at itesm.mx>
  • Date: Sat, 6 Dec 2008 06:14:01 -0500 (EST)
  • References: <200812051033.FAA25101@smc.vnet.net>

Interesting question, I do Not know if it is possible (or practical) to do
it with the built-in command Inverse, I believe that command was made for
working with matrices of Complex numbers, maybe it would be better to create
your own program in Mathematica for this kind of calculations.

In order to create this program, you could use an approach similar to the
one shown in this part of the documentation:
http://reference.wolfram.com/mathematica/tutorial/AnExampleDefiningYourOwnIn
tegrationFunction.html 

Here I have another version of the "Defining your own Integration Function"
in Spanish. Even if you do Not understand Spanish, the step-by-step approach
might be useful for you:
http://homepage.cem.itesm.mx/jose.luis.gomez/global/50aprendiendoaintegrar/5
0aprendiendoaintegrar.html 

Finally, if the noncommutativity you are working with has some relationship
with Quantum Mechanics and/or Hilbert spaces, you might consider using our
Quantum Mathematica Add-on for your calculations:
http://homepage.cem.itesm.mx/lgomez/quantum/ 

Hope that helps
Jose
Mexico

 
-----Mensaje original-----
De: Steven Allmaras [mailto:steven.r.allmaras at boeing.com] 
Enviado el: Viernes, 05 de Diciembre de 2008 04:33
Para: mathgroup at smc.vnet.net
Asunto: [mg94126] symbolic matrix inverse

I have a symbolic matrix {{a,b},{c,d}} whose elements are themselves
matrices.  The elements are noncommutative (e.g., a.b != b.a), and just for
simplicity assume each element is a n-by-n square matrix of reals.  How do I
get Mathematica to evaluate Inverse[{{a,b},{c,d}}] in terms of Dot and
Inverse, rather than Times and Divide?  I'm hoping to get something that
looks like,

[[1,1]] = Inverse[a] + Inverse[a].b.Inverse[d - c.Inverse[a].b].c.Inverse[a]

Thanks,
Steve





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