On the Algebraic Derivation of the State Equations

State equations such that the state vector is composed exclusively of currents in inductances and voltages across capacitances have been obtained in the past by topological methods. The same result as well as an extension thereof to general finite lumped constant linear systems can be achieved by algebraic methods. The only requirement is that these systems are well defined, i.e., such that they represent a meaningful model of an actual physical system.