Note that the new matrix m is symmetric! cij is symmetric indeed for heat flow problems and most other physics problems where reciprocity reigns.
Let D be a diagonal matrix where Dii = 1/Ci. We may now write the matrix equation m = DC (this is a different m!! Fix! ....) and use this code to compute eigenvectors and values for m.
We find g so that gmg−1 is diagonal with diagonal elements dj.
If Ej is the jth basis vector in the new coordinates then our general solution to the equations is:
ΣjajEjedjt. The n reals aj are the parameters to the solution.