Customer Reviews

Linear Algebra & Its Applications: Custom Edition for the Univeristy of Buffalo

5 star:		(13)
4 star:		(20)
3 star:		(5)
2 star:		(5)
1 star:		(6)

 

 

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.

I used this as the textbook for an undergraduate course in Linear Algebra. It was by far the most reader-friendly math book I've ever had the pleasure of using. The book explains Linear Algebra in plain, easy-to-read english. Each section of each chapter is very clear and to-the-point. The examples are helpful and well-placed in the chapters. I attribute getting an 'A' in that class to this text.

One word of advise however... the study guide for this text comes in handy at numerous points of the book. It's not needed, but strongly advised. Other than that, the book is great! I only wish that I had a calculus book that well written.

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.

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).

Filling a book with applications is no good when you compress the theoretical material. This book, although nice on the application side, falls short when the going starts to get rough.
This book has chapters that are not even worth reading, like the chapter on Eigenvectors and Linear Transformations. In general, the explanations are so short or lack demonstrations to a point where you end up memorizing theorems (a demonstration is not a paragraph in cursory English saying "blah, blah, as we saw previously, blah, blah, blah." If you doubt me, do that on an exam and see what the professor writes in red ink, later). Is that what you want ? The serious student will then waste his/her precious little time trying to fill in the gaps with other books. I'm not even talking from the standpoint of abstractness and rigour. I'm just saying explanations are lacking.
A reviewer said some problems are hard to do with the text, and 98% are done by rote. This is correct. The "hard" problems are hard because the book is lacking in abstraction. Another reviewer said this book will please engineers more than mathematicians. I feel this is correct too. Applied mathematics students should also avoid this book. I don't think this book prepares you for "the next level", where you'll be working with real problems. I don't see this book preparing the student for computational linear algebra, and I don't think there's nearly enough matrix theory here. Also, I think the book has that American textbook style where things are broken into small pieces and fit into nice-looking boxes and the text tends to loose its flow and you tend to loose the conections. It's not a good writing style for my taste.
It's kind of like a Calculus book. They lie to you first, and then they teach you "Advanced Calculus" and "Analysis." Personally, I don't like that approach, because I think it's a time waster. And, you might not get a second chance to ge it right as an undergraduate (this is true for engineering students at my institution).
Quickly immerse yourself in "Matrix Analysis and Applied Linear Algebra" by C. D. Meyer and avoid this book; or, another great book (and everybody says so, because it is), Gilbert Strang's "Linear Algebra and Its Applications." The virtues I see on this book are carefully chosen illustrations that help to convey meaning to the theorems by geometric aid and the intertwined applications "appetizers."
All in all, though, it'll do you more harm than good. Students who enjoyed this book have probably haven't read any other.
This review refers to the 2nd edition.

Lay presents here a basic textbook on linear algebra. Topics covered include matrices, determinants, vector spaces, eigenvalues & eigenvectors, and orthogonality. As a student of economics, I was happy to see that a few of the applications of linear algebra presented are related to economics and statistics (the Leontief Input-Output Model in Chapter 2, for example).

When I first encountered this book in an undergraduate matrix algebra course, I found it to be quite accessible despite my liberal arts background. More recently, since I have been a graduate student, the book has proven to be a decent reference for the basics of linear algebra, although I wish it covered projections in more detail -- particularly non-orthogonal projections.

From an economist's point of view, I would sum this book up as follows: it covers enough material to address linear algebra concepts needed in a first-year graduate microeconomics course, but not enough for a first-year graduate econometrics course.

The last time I wrote a review for this book, I gave it 2 stars; now, after going through the whole book, I'm able to give it 5 stars. No matter what your major is, and no matter how advanced you are, this book has something. It is example-oriented, easy to follow, and right to the point. Each chapter starts off with theory and ends with applications. Each section starts with basic definitions and easy problems and ends with theorems and harder probrems. The 2nd edition is pretty much the same as the 3rd edition, so don't waist money for nothing.

The book is good, probably better than I think. I blame much of my bias on the (visiting) prof I had for this intro class. She didn't like the way the book was organized and insisted on jumping around - quite a difficult way to use a math text unless you already know the material.

I didn't think the organization was bad. As an undergrad econ major I understood the progression. Unfortunaely I think the coverage in some areas is too concise and sometimes the book fails to tie ideas together. As someone else noted, the proofs are passable but not great. The book lends itself to a variety of majors, whether math, econ, physics, business, etc. as there are a number of good examples.

My biggest gripe is with the answers in the back and the answer/study guide. I'm sorry if Dr. Lay's students are too lazy to actually do the work and reading and would prefer to look in the back, but christ allmighty, please provide the answers *and* reasons for the answers for T/F questions. If the T/F questions are important enough to include in virtually every section then don't you think we should have the answers? The answer/study guide is virtually worthless. Look, I played the game and plunked down the extra bucks for the study guide, so would you please give me the solutions? I don't like getting the run-around if I don't understand something. Using the guide is like something out of a monty python skit. So for these reasons the book gets rated down a star.

I used it in a linear algebra class when I was an undergraduate at Cornell. I found out that it was a very readable and useful reference for concepts and theories. The book is very organized; and it's such a good start for people who are interested in learning linear algebra. Believe me! U won't be disappointed!!!

I used this as the textbook for an undergraduate course in Linear Algebra. It was by far the most reader-friendly math book I've ever had the pleasure of using. The book explains Linear Algebra in plain, easy-to-read english. Each section of each chapter is very clear and to-the-point. The examples are helpful and well-placed in the chapters. I attribute getting an 'A' in that class to this text.

One word of advise however... the study guide for this text comes in handy at numerous points of the book. It's not needed, but strongly advised. Other than that, the book is great! I only wish that I had a calculus book that well written.