Finite Dimensional Linear Operators in the Problems of the Theory of Electrical Circuits

Abstract

The paper is devoted to substantiation of Intermediate Problem method for multi loop electrical circuits’ analysis. All pure-loop
and pure-nodeircuits contained in the group GC of the initial primitive circuit possess pairwise equal eigenvalues equal in their
turn to the eigenvalues of the primitive circuit. The matrices of impedances and conductances and are reciprocal, i.e. is the
resolvent of , and vice versa. The Weinstein function for the LC-circuit described by the loop matrix Z(k) is the determinant
of a lower right submatrix of order n-k. The Weinstein function for the LC-circuit described by the node matrix Y(n-k) is the
determinant of an upper submatrix of order k of the resolvent Zn lying at the intersection of the first k rows and columns of the
matrix Z(n) . The determinant of the conductance node matrix of an arbitrary k-loop LC-circuit is the Weinstein function for the
loop impedance matrix of this circuit, and vice versa.