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!