Applications of the theory of matrices to electric networks



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The objective of thia thesis is the investigation of the application of the theory of matrices to analysis of electric networks. Various theorems from the theory of matrices which are applicable to matrix analysis of electric networks are stated and proved in Part I. Part II, Chapters III and IV, consists of problems of electric network theory whose solutions are facilitated by use of the theory of matrices. Using matrix methods, the mesh and node pair equations are developed and solved In Chapter III. Applications of matrix methods to transmission networks and transmission lines are considered in Chapter IV. It is the opinion of the author that the method of developement of equation (3.2.13), Theorems 4.1.1 and 4.2.1, and the proofs of Theorems 4.4.1 and 4,4.2 are original contributions. Equation (3.2.13) is one of the principal equations used in node pair analysis of electric networks. Theorems 4.1.1 and 4.2.1 are concerned with the matrix associated with a transmission network. Some interesting properties of a particular matrix are stated in Theorems 4.4.1 and 4.4.2. This matrix is useful in the analysis of fully transposed transmission lines.