Matrices in Engineering

IT IS THE purpose of this paper to develop in a concise and simple manner the theory of matrix algebra from the foundations, and to emphasize the use of this powerful method in engineering problems. It appears not to be a well-known fact among engineers that the matrix is not only a convenient notation that summarizes in a natural and convenient form whole groups of operations but that it is actually possible to solve the sets of differential or algebraic equations written in matrix form in a most convenient manner. The method by which this is done is one of the utmost simplicity but makes use of some fundamental theorems on matrices not usually found in texts. The theory is scattered throughout the mathematical literature. It has, therefore, been considered worth while in the interest of unity and simplicity to build the subject from the foundations. It thus requires no previous knowledge of matrix algebra for the understanding of this paper. The recent work of Kron, Sah, and others using the notation of tensors and dyadics in studying the behavior of circuits and machinery suggests the power and flexibility of more advanced mathematical methods in expressing the behavior of physical systems. A perusal of this paper will illustrate that the matrix appears to be a natural tool to employ in the solution of certain classes of problems.