Certain applications of matrices to circuit theory

This paper is intended to show the intimate relationships between the eigenvalues and eigenvectors of certain matrices and some well-known electrical parameters such as propagation constants, characteristic and iterative impedances in single-phase systems, and symmetrical components in polyphase systems whose impedance matrices have circular symmetry. The basic ideas are applied to show how Lucas functions, and the polynomials of Chebyshev and Gegenbauer enter naturally in the discussion of the propagation of potentials and currents along chains of identical and geometrically tapered quadripoles.