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I'd like to compute the centralizer of a subgroup $H$ of orthogonal group $O(8, R)$, so I need to solve the equation $AX=XA, BX=XB \mbox{ where } H=\langle A, B\rangle.$ The problem that I have is matrices A and B are symbolic, in fact their entries are for example$(\cos \frac{1}{n})$ or $(\sin \frac{1}{n})$. I think the command lyap can help me, but in all examples that I have seen matrices $A$ and $B$ have been numerical not symbolic. I will appreciate any comments and help to solve this problem.

dtldarek
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Jayq
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  • Although Matlab has a symbolic package, I'd recommend to use Mathematica, Maple or any other analogous software. – Kaster Aug 01 '13 at 07:58
  • @nanthini You can use \langle and \rangle to produce $\langle A,B \rangle$ instead of $<A,B>$ which looks weird (and the spacing is wrong). Also (from your previous edits) it's better to use \frac $\frac{x}{y}$ instead of \over ${x \over y}$ and \mathbb $\mathbb{R}$ instead of \Bbb $\Bbb{R}$. – dtldarek Aug 01 '13 at 09:11
  • @dtldarek okay i will correct it – nanthini Aug 01 '13 at 09:23
  • @Kaster: You recommend other software, but don't say anything about how they're suitable to this problem. The thing about Matlab's Symbolic Toolbox is that it supports much of the same matrix math that the rest of Matlab does. – horchler Aug 01 '13 at 16:53
  • lyap is in the Control Systems toolbox. Assuming that this is a Lyapunov system, and you want to use Matlab, you'll need to write some code. Here's a paper entitled Solving Lyapunov equations symbolically that might help - it includes simple Maple code that you could probably decipher and translate into Matlab. – horchler Aug 01 '13 at 17:06
  • @horchler, in my personal opinion based on experience, Mathematica is more suitable for any kind of symbolic calculations than Matlab with its symbolic toolbox. – Kaster Aug 01 '13 at 17:16
  • @Kaster: That's fine, but without providing any sort of real information, your comment is tangential to the question when you don't even know if the OP has access to Mathematica or Maple or if they are solving this problem in the context of a larger one using Matlab. I was only suggesting that your comment could be more helpful. – horchler Aug 01 '13 at 17:37
  • @Masoumeh: is Mathematica or Maple an option for you in solving this or must you use Matlab? In Mathematica you might have a look at LyapunovSolve. – horchler Aug 01 '13 at 17:38
  • @Horchler: I can use any software. I even tried GAP, but it works for finite fields. – Jayq Aug 02 '13 at 09:34
  • @All: Thank you very much for helpful comments. I'd try Maple or Mathematica. – Jayq Aug 02 '13 at 09:36
  • @Masoumeh Mupad of MATLAB is designed to do symbolic operations. You can type mupad in command window to use it. – Mahdi Khosravi Aug 07 '13 at 07:33

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