Linear Algebra: Ideas and Applications

By Richard C. Penney and Richard C Penney

Book Overview

This expanded new edition presents a thorough and up-to-date introduction to the study of linear algebra Linear Algebra, Third 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, the book successfully helps readers to understand not only how to implement a technique, but why its use is important. The book 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 Third Edition also features: A new chapter on generalized eigenvectors and chain bases with coverage of the Jordan form and the Cayley-Hamilton theorem A new chapter on numerical techniques, including a discussion of the condition number A new section on Hermitian symmetric and unitary matrices An exploration of computational approaches to finding eigenvalues, such as the forward iteration, reverse iteration, and the QR method Additional exercises that consist of application, numerical, and conceptual questions as well as true-false questions Illuminating applications of linear algebra are provided throughout most parts of the book along with self-study questions that allow the reader to replicate the treatments independently of the book. Each chapter concludes with a summary of key points, and most topics are accompanied by a "Computer Projects" section, which contains worked-out exercises that utilize the most up-to-date version of MATLAB(r). A related Web site features Maple translations of these exercises as well as additional supplemental material. Linear Algebra, Third Edition is an excellent undergraduate-level textbook for courses in linear algebra. It is also a valuable self-study guide for professionals and researchers who would like a basic introduction to linear algebra with applications in science, engineering, and computer science.

• Format: Hardcover
• Language: English
• ISBN: 0470178841
• ISBN13: 9780470178843
• Release Date: July 2008
• Publisher: John Wiley & Sons Inc
• Length: 480 Pages
• Weight: 1.87 lbs.
• Dimensions: 9.3" x 1.0" x 6.5"

Customer Reviews

Great for transitioning to abstract math

All right, I'll admit it: when it came to math, for most of my life I was a ninety-eight-pound weakling. I excelled at analogies, reading comprehension, vocabulary, people called me "Verbal" -- but when it came to equations and theorems, I was useless. At the same time, I was fascinated by math, resulting in my picking up quite a number of algebra and analysis books I was woefully unprepared to comprehend. This book changed that. I took a linear algebra class where it was the assigned textbook, and for the first time I would read the textbook to understand what was going on in class, not the other way around. The particular strength of this book is in encouraging what is called "mathematical maturity" (usually cited as a "prerequisite" in the introductions to books on higher mathematics). Mathematical maturity is not simply a "formal" grasp of mathematical operations: learning how to formalize the Peano axioms in a logic class won't cut it. It's about learning how to balance mathematical exigency with theoretical elegance, and this book is specifically designed to get you to grasp such issues. It does this by emphasizing the importance of proofs, without forcing you to deduce all necessary principles from axioms. In this, it differs quite markedly from other introductory linear algebra textbooks, such as Howard Anton's. Anton et al., like calculus and high school algebra texts, are designed in a "cookbook" format: they offer you numerical recipes for getting desirable outcomes from given data. That is not to say they are uniformly less advanced: Anton's text covers topics, like the Vronskian, which this textbook does not. And on the other side of the scale, there probably isn't much difference if you only want to learn Gaussian elimination. However, if you're in the market for a linear algebra textbook, you are probably needing to grasp not only matrix operations but also how mathematics proceeds beyond solving equations: and I can tell you from experience, learning from this book is one of the easiest ways to do so. For someone with a year of calculus under their belt, a course using this book would be an excellent choice: the book would also be cost-effective for self-study by a person with a little money but not much time. Errors are commonplace in any textbook in the exact sciences: a program for making essential skills comprehensible to many is rare indeed.