Linear Algebra and Its Applications (3rd Edition) (Hardcover)

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Product Description

Linear algebra is relatively easy for students during the early stages of the course, when the material is presented in a familiar, concrete setting. But when abstract concepts are introduced, students often hit a brick wall. Instructors seem to agree that certain concepts (such as linear independence, spanning, subspace, vector space, and linear transformations), are not easily understood, and require time to assimilate. Since they are fundamental to the study of linear algebra, students' understanding of these concepts is vital to their mastery of the subject. Lay introduces these concepts early in a familiar, concrete Rn setting, develops them gradually, and returns to them again and again throughout the text. Finally, when discussed in the abstract, these concepts are more accessible.

About the Author

David C. Lay holds a B.A. from Aurora University (Illinois), and an M.A. and Ph.D. from the University of California at Los Angeles. Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has also served as a visiting professor at the University of Amsterdam, the Free University in Amsterdam, and the University of Kaiserslautern, Germany. He has over 30 research articles published in functional analysis and linear algebra.

As a founding member of the NSF-sponsored Linear Algebra Curriculum Study Group, Lay has been a leader in the current movement to modernize the linear algebra curriculum. Lay is also co-author of several mathematics texts, including Introduction to Functional Analysis, with Angus E. Taylor, Calculus and Its Applications, with L.J. Goldstein and D.I. Schneider, and Linear Algebra Gems-Assets for Undergraduate Mathematics, with D. Carlson, C.R. Johnson, and A.D. Porter.

A top-notch educator, Professor Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar-Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America's Awards for Distinguished College or Unviersity Teaching of Mathematics. He has been elected by the university students to membership in Alpha Lambda Delta National Scholastic Honor Society and Golden Key National Honor Society. In 1989, Aurora University conferred on him the Outstanding Alumnus award. Lay is a member of the American Mathematical Society, the Canadian Mathematical Society, the International Linear Algebra Society, the Mathematical Association of America, Sigma Xi, and the Society for Industrial and Applied Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.

Product Details

• Hardcover: 576 pages
• Publisher: Addison Wesley; 3 edition (July 18, 2002)
• Language: English
• ISBN-10: 0201709708
• ISBN-13: 978-0201709704
• Product Dimensions: 9.5 x 8.2 x 1 inches
• Shipping Weight: 2.4 pounds
• Average Customer Review: 3.5 out of 5 stars  See all reviews (45 customer reviews)
• Amazon.com Sales Rank: #196,290 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

12 of 13 people found the following review helpful:

4.0 out of 5 stars For what it is, this book does its job., November 19, 2005

By	Dingo Jellybean (Silver Spring, MD) - See all my reviews

Being a University of Maryland student and a math major, I've actually had this author as my professor. He's a great professor and a distinguised scholar-teacher at the University and really knows how to convey the material well.

But I think the professor is a better instructor than the book. This isn't an insult to the book, because he's an excellent professor.

I've seen reviews for this book that were pretty unfavorable. Some of them were just reviews, some unjust. People need to realize that this book is just an introduction to Linear Algebra, it is a book for lower level undergraduate mathematics. This course is equivalent to a freshman calculus course; it is mainly to teach you to do calculations and apply them. Some of the reviews treat this book as if it were for some upper level class like Abstract Linear Algebra (which is a much tougher course and requires a deeper book).

But for what it is, the book is clear in most cases. But like people mentioned, the Invertible Matrix Theorem is scattered about the book but never summarized. There are a few tough exercises, but 98% of all exercises in the book can be completed via the examples given in each chapter...just like a freshman calculus text. I don't think the book is a hard read, it's pretty easy in fact, but it won't really help you out much to prepare for proof-oriented classes like Number Theory or Advanced Calculus. This book will benefit engineers more than it will mathematicians. The true/false questions themselves are not too helpful in my opinion. The answers to these are vague and refer you to the study guide (which in turn are not direct answers, but more like indirect answers and probably a cheap way to plug in his study guide). The study guide itself will contain 1/3rd of the odd answers in the book and are clear to read and will review some of the chapters' key concepts in different wording. But most math majors probably won't need this study guide. The study guide is mainly for students who won't be majoring in math (I.E. computer science, physics, engineering, etc.).

The book doesn't go too much into proofs. Most of the proofs are trivial to prove, so there is no need to really have an entire chapter devoted to developing proof skills. However, most students taking this course have no idea of what a mathematical proof is. This book gives a bad impression of what a proof is. The proofs in this book mostly deal with "DE' = AC --> D = ACE", which is just algebraic manipulation. Any student hoping to jump into a proof oriented class using this book will be sorely lacking. But let's give the author credit. He never intended this book to prepare students for that "next-level" of mathematics (I.E. writing rigorous proofs). His intent, and I've had this professor, was mainly to teach linear algebra in a way that would draw students towards mathematics and see how the world of linear algebra is an exciting one. For this, I think he's done just that.

15 of 17 people found the following review helpful:

2.0 out of 5 stars From an instructor's point of view, February 24, 2001

By A Customer

This review is from: Linear Algebra and Its Applications (Hardcover)

I used this book for several years in my Linear Algebra. It suffers from many of defects that all Linear Algebra texts at the level suffer from these days. The first Chapter introduces the concept of linear independence without suitably introducing vectors. Linear transformations are also introduced in this chapter, again without the proper tools to deal with it. Another topic in this Chapter is the solution of systems of Linear Equations. The treatment of the case where there is more than one solution is totally and hopelessly inadequate. The method used to generate the solution does nothing but confuse the students.

Chapter 4 is far too laconic. The treatment of projections lays no foundation, does not connect it with eigenvalues but just jumps into orthogonal bases. It is difficult believe that anyone would guess that orthogonal matrices are important from the information given in this book. The treatment of least squares is too sparse.

The treatment of Linear Transformations is extraordinarily lacking. The treatment of the kernel and image lead no place. There are insuffient number of examples and relation to geometric concepts.

Unfortunately, almost all new texts in this field are just as bad.

9 of 10 people found the following review helpful:

5.0 out of 5 stars Outstanding linear algebra text !!, December 4, 2002

By A Customer

I am currently about a week away from completing a course in which we've used this next (the THIRD edition). I cannot express enough the unbelievable level of quality and attention to instruction that has been put into this edition. I cannot speak for previous editions, and from some of these comments it doesn't sound as those past versions of the text are anywhere near as good as the third edition.

For what it's worth, I strongly suggest that anyone needing a secondary text for a linera algebra course consider this book. It may be pricey, but there's no way I'm letting this one go after the semester is over. It's going on my shelf and staying there!

This book has more visual, geometric interpretations and depictions that you'd ever find in another book, and what's more it's actually concise. You don't get 10 pages of explanation when one or two will suffice. Concepts are continually reinforced and re-examined, not to mention built upon. You will continuously be presented with the links between chapters and concepts, and this is one of the book's greatest strengths. When you get to see how it all fits together, it sincerely improves the learning experience. The subject matter becomes not 7 distinct chapters of abstract methodology, but instead 7 parts of the same story. You'll know why you're doing things a certain way, and when you read the material in chapter 5, for example, you'll fully and readily understand why you learned chapters 1 thru 4 first, not to mention how the material there fits with the ideas in later parts of the book.

Previous reviewers were right, you sincerely can injoy reading parts of this text, if not all of it. The examples are painfully clear even to the uninitiated. I honestly believe that if you cannot learn from this book, there is no hope for you. Take it from me, I'm not a math person at all, and yet I'm getting an A in the course thanks entirely to this book.

Following lecture I've gone home, cracked open the text and been able to do the entire homework assignment without taking a single peek at my notes from class. The instruction and examples in the text are truly all that you need to work the problems. Yes, it's THAT good. Proofs abound, but they are easy to follow and really help to enforce concepts and the inter-relation between ideas. I dare say the proofs even help you remember why certain definitions are what they are, rather than the sophmoric method of memorization.

This book is a steal at twice the price, do yourself a favor and check it out. Please don't be influenced by poor reviews of the previous "hardback" edition, because the new third edition is nothing like that others have commented. Judge for yourself, skim through it a bookstore first or whatever, but don't pass this up just because some halfwhit that failed the course decided to run his mouth on amazon (see below).