Matrix factorization

A PRECISION approach to network analysis is obtained through the use of network topology and matrix algebra. A study of the mathematical properties of the matrices resulting from such an approach brings to light many interesting facts. In particular, a study of the matrices arising in network analysis that contain linear factors in the lines of the matrix yields a number of interesting and useful results. The method of approach in this paper is to first develop a group of theorems setting forth various properties of matrices that arise in the m (mesh) and n (node) systems of equations. Then these properties are used to prove an additional group of theorems relating to a matrix inverse which occurs in the solution of any of these systems. Finally the results of these theorems are related to the solutions of the network equations and to the networks themselves. A discussion is then presented of the application of these results in network design, network analysis, and network correction.