Linear Algebra: Ideas and Applications

by Richard C. Penney and Richard C Penney

Book Overview

A student-oriented approach to linear algebra, now in its Second Edition This introductory-level linear algebra text is for students who require a clear understanding of key algebraic concepts and their applications in such fields as science, engineering, and computer science. The text utilizes a parallel structure that introduces abstract concepts such as linear transformations, eigenvalues, vector spaces, and orthogonality in tandem with computational...

• Format: Hardcover
• Language: English
• ISBN: 0471676209
• ISBN13: 9780471676201
• Release Date: August 2004
• Publisher: Wiley
• Length: 450 Pages
• Weight: 1.68 lbs.
• Dimensions: 1.0" x 6.1" x 9.6"

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.