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I have the following symmetric system:

$$f_i = \sum_j^n \tau_{ij}c_j^{-1}y_j$$ $$c_j = \sum_i^n \tau_{ij}f_i^{-1}y_i$$ $$\tau_{ij}=\tau_{ji}$$

$$F = \left[ \begin{matrix} f_1 \\ ... \\ f_n \end{matrix} \right] $$

$$C = \left[ \begin{matrix} c_1 \\ ... \\ c_n \end{matrix} \right] $$

and how to solve the $f_i$ and $c_i$?

Does this two equations have the reduced form relationship?

Is there any theory that relate to such kind of symmetric system?

Thank you!

XJ.C
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    Can this system be readily transformed into a set of matrix equations? Also, what is the dimension of the system, Do both summation indices run to, say, $n$? –  Jul 21 '16 at 07:54
  • Yes, it can be transformed into a set of matrix equations. – XJ.C Jul 21 '16 at 07:58

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