Linear Algebra ─ Ideas and Applications

Linear Algebra: Ideas and Applications, Fourth Edition provides a unified introduction to linear algebra while reinforcing and emphasizing a conceptual and hands-on understanding of the essential ideas. Promoting the development of intuition rather than the simple application of methods, this book successfully helps readers to understand not only how to implement a technique, but why its use is important. In addition, the author outlines an analytical, algebraic, and geometric discussion of the provided definitions, theorems, and proofs. For each concept, an abstract foundation is presented together with its computational output, and this parallel structure clearly and immediately illustrates the relationship between the theory and its appropriate applications. The Fourth Edition features new coverage on orthogonal wavelets, which is a cutting edge application of linear algebra that has only become prominent within the last 10 years. The text is complete with applications when and where appropriate. Most sections are followed by at least one application section, which includes two different types of exercises: Self-Study Questions and Exercises. The exercises have been greatly increased and consist of application, numerical, and conceptual questions, and each exercise section begins with True-False questions. A Student Solutions Manual containing solutions to the odd numbered problems is available to further aid in reader comprehension, and an Instructor's Solutions Manual (inclusive of suggested syllabi) is available via written request to the Publisher. Both the Student and Instructor Manuals also have been enhanced with further discussions of the applications sections, which is ideal for readers who wish to obtain a deeper knowledge than that provided by pure algorithmic approaches. A related website houses the referenced MATLAB code as well as full-color images of select figures.

Richard C. Penney, PhD, is Professor in the Department of Mathematics and Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher.