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MathGroup Archive 2005

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Matrix equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53862] Matrix equations
  • From: Jamie Vicary <jamievicary at gmail.com>
  • Date: Tue, 1 Feb 2005 04:08:12 -0500 (EST)
  • Organization: University of Cambridge, England
  • Sender: owner-wri-mathgroup at wolfram.com

Hi there,

     I'm using Mathematica 5.1 and trying to solve equations like the 
following:

         A.{{1,0},{0,2}} == -{{1,0},{0,2}}.A

i.e. I want to find the matrix that anticommutes with {{1,0},{0,2}}. The 
only matrix that solves this is the zero matrix {{0,0},{0,0}} but 
Mathematica refuses to solve the above equation for A, giving the usual 
"The equations appear to involve the variables to be solved for in an 
essentially non-algebraic way."

     If I set A={{a,b},{c,d}} and then solve the above equation for 
{{a,b},{c,d}} then Mathematica correctly tells me {{a->0, b->0, c->0, 
d->0}}, but this isn't what I want. I want to give Mathematica equations 
in terms of matrices, not in terms of their components.

     In summary: why, when I give Mathematica the above equation to 
solve for A, does it not solve it giving A->{{0,0},{0,0}} which is the 
trivial, unique solution to the equation?

         Thanks,

             Jamie Vicary.


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