Functional-matrix theory for the general linear electrical network. Part 3: Eigenvector method for inversion of the general functional matrix

The general functional matrix has the computational disadvantages of increasing rapidly with system order and of having large numbers of zero elements. If a spectral analysis of the linear functional matrix is available, these disadvantages may be overcome by making use of relationships between the dyadic expansion of a matrix and the dyadic expansions of its inverse powers. A set of tables is given which shows the eigenvectors and reciprocal eigenvectors of the general functional matrix in terms of those of the linear functional matrix. These tables thus provide an alternative means of computing the functionals considered in the two previous papers.