Part I — Matrix operations and generalized inverses

The theory of matrices is playing a role of rapidly increasing importance in the formulation and solution of problems, not only in mathematics and engineering, but in the biological and social sciences as well. Before the advent of the computer, a mathematician could talk glibly about the existence and uniqueness of a solution of a system of ten linear equations in ten unknowns. Few had ever tried to find the solution of such a system. Now matrix theory not only provides an extremely helpful tool for designing a mathematical model of a system with many variables, but also affords a practical and convenient method of adapting the data for processing by a computer. The theory of functions of a matrix — including polynomial, exponential, and trigonometric functions — provides an extremely powerful tool both for model making and for providing numerical answers. Some feel that any problem that can be solved by Laplace transform methods can be solved with equal or greater ease by using functions of matrices.