Determination of the capacitance matrix

The scalar potential on any conductor can then be determined by adding the contributions due to the charges on all conductors (including that conductor itself). The relationship is linear and can be expressed in matrix form.

$$\mathbf{V} = \left[ G _{I} \right] \mathbf{q}$$ (8)

The vector of scalar potentials, of which each element is just the scalar potential on a particular conductor, is equal to a square coefficient matrix times the vector of charges. The capacitance matrix is then determined by inverting that coefficient matrix.

$$\mathbf{C} = \left[ G _{I} \right] ^{-1}$$ (9)