dT

(dt

dt

dt

dt

dt

dt

Note that the new matrix m is symmetric!
c_{ij} is symmetric indeed for heat flow problems and most other physics problems where reciprocity reigns.

Let D be a diagonal matrix where D_{ii} = 1/C_{i}.
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 d_{j}.
If E_{j} is the jth basis vector in the new coordinates then our general solution to the equations is:

Σ_{j}a_{j}E_{j}e^{djt}.
The n reals a_{j} are the parameters to the solution.