Uniqueness of solutions of piecewise linear resistive networks with two terminal resistors

Consider a network comprising two terminal linear, piecewise linear resistors and independent sources. Contrary to widely held belief, it is shown that the determinant sign condition (i.e. the Jacobian determinant is nonzero and has the same sign in all the regions) is both necessary as well as sufficient to guarantee uniqueness of solutions of these networks. For this purpose the existence of a specific hybrid matrix is not required