Wed Nov 5 00:05:11 EST 2014

Symmetric conductivity matrix

Trying for a maximally connected 3-node network 0,1,2.  Node 0 is the
ground node, giving two variables V10, V20.  The effect of a current
source connected between node 1 and 2 can be absorbed into current
sources from ground to nodes 1,2.  This gives the following equations:

G V = I

(G10 + G12) -G12          V10   I01   
-G12        (G20 + G12)   V20   I02

With Gxy conductivity between node x and y.
     Ixy current flowing from x to y
     Vxy voltage drop from x->y

Where does this symmetry come from?
Essentially from the symmetric relation "connected to".

I.e. a resistor doesn't have any sense of direction.

This generalizes to

a_xx = Gx0 + \sum_y!=x Gxy
a_xy = -Gxy                (x != y)