Properties of the generalised inverse matrix in the electrical-network problem

A modified form of Roth´s transformation diagram for a linear graph is used to illustrate the solution of the electrical-network problem. The diagram illustrates particularly the significance of the orthogonal projections of the branch space into the branch voltage and current subspaces, which are defined by Kirchhoff´s laws, and also the existence of the constrained matrix inverse which forms a basis for the solution of the electrical-network problem. Properties of the generalised inverse matrix are also discussed in relation to the network problem.