Hadley G. Linear Algebra

Reading: Addison-Wesley, 1977. — 298 p.Classical text on linear algebra.In recent years, linear mathematical models have assumed an important role in almost all the physical and social sciences, and as was to be expected, this development has stimulated a remarkable growth of interest in linear algebra. It is therefore surprising that the number and variety of volumes written on linear algebra seem not to have kept pace with the diversified needs of those in such fields as mathematics, engineering,economics, operations research, and business. This text, however, represents an effort to meet the needs not only of those studying mathematics,but also of those working in the physical and social sciences. It is intended to be a reasonably rigorous, but not abstract, text. It was written with the intention that it could be read and used by those with a limited mathematical background. An attempt has been made to introduce new ideas slowly and carefully,and to give the reader a good intuitive "feeling" for the subject. The abstract axiomatic development, while it has many things to recommend it,did not seem appropriate here and was not used. Many numerical examples are given and, insofar as possible, each important idea is illustrated by an example, so that the reader who does not follow the theoretical development may assimilate the material by studying the example. For simplicity, all scalars in the text are assumed to be real numbers, although it is pointed out in appropriate places that the results hold for complex numbers as well. However, the author believes that students,especially engineers and physicists, should have the opportunity to solve problems involving complex numbers, and therefore such problems are included at the end of the appropriate chapters. It is interesting to note that in many mathematics texts which are more general in their presentation and allow the scalars to be elements of a field, it is not possible to find a single problem requiring the use of complex numbers.Those who expect to make use of linear algebra must have some awareness of the problems involved in making numerical computations. Consequently, numerical techniques are discussed in somewhat greater detail than is usual. A novel feature of the text is the inclusion of a chapter covering certain topics in convex sets and n-dimensional geometry. It also contains an elementary discussion of some of the properties of sets of linear inequalities.The author considers the problems at the end of each chapter to be very important, and the reader should examine all and work a fair number of them. They contain additional theoretical developments as well as routine exercises.This text might be used in a variety of ways: for a one-semester or one-quarter course in linear algebra; as a text or reference for part of a course in engineering mathematics, mathematical physics, or mathematical economics; as a supplementary text for courses in linear programming, quantum mechanics, classical mechanics; etc.