User:DVD206/Y-Δ and star-mesh transforms

The effective conductivities and the Dirichlet-to-Neumann operator of a network are invariant under the following star-mesh transform,

Exercise (**). Use the Schur complement formula

$\Lambda =K/C$

for the Dirichlet-to-Neumann map to prove the invariance.

The Y-Δ transform is a special case of the star-mesh transform in which the center node has the degree 3.