The gauss elimination from the circuit theory point of view: Diagonal nodal equivalent

Nodal analysis is known to be the most used method to write the solving equations of electrical circuits. The matrix equation is usually solved by using Gauss elimination (GE). This paper studies in depth the GE from a circuit theory point of view. It results that each step of GE constitutes a modification of the assigned circuit. The forward elimination can be considered as a successive removal of the independent nodes by introducing voltage-controlled current sources, while back substitution leads to independent elementary circuits. The whole procedure can be systematically applied; in this way, given a circuit, it is possible to switch to a modified circuit, by means of circuital transformations corresponding to mathematical ones. Similar approach can be used also when the mesh analysis is used to solve a circuit. In this case the forward elimination can be considered as a successive removal of the independent meshes by introducing current-controlled voltage sources.