Customer Reviews

Linear Algebra and Its Applications, 3rd Updated Edition (Book & CD-ROM)

5 star:		(17)
4 star:		(10)
3 star:		(3)
2 star:		(5)
1 star:		(9)

 

 

I am just finishing up an introductory Linear Algebra course using this book. I am a mechanical engineering student, and not a math major, so keep that in mind when reading this review.

I personally really liked Lay's approach and writing style. The first chapter is a basic overview of linear algebra and helps you start to see what linear algebra is all about immediately.

I also like Lay's method of highlighting important theorems and definitions. He uses a light blue background for theorems and key ideas and a greenish type color for definitions. Very helpful for studying and you don't have to dig through the text to find the main topics. There is also a glossary, something that seems kind of rare in math textbooks and I really liked having.

I liked the practice problems before each problem set, they were kind of like examples, except the solution was on a different page. Also, row operations in this text always work out nicely, which means I didn't struggle with difficult computations that need not be difficult and cloud the concept I was trying to learn.

I didn't feel like there was enough problems. For each section there was about 10-20 problems computational problems, some true/false questions, and about 10-15 or so questions that either asked you to prove things or were applied problems. I wish there was twice the amount of problems, I'm the kind of student who needs lots of practice.

The invertible matrix theorem should of been summarized in its entirety somewhere. Its scattered across 6 sections in 5 different chapters.

I feel the book is really good for engineering students and applied math majors. Pure theoretical math majors, I could see how you might not like this book. The text doesn't seem that abstract and you aren't buried in proofs, but I believe Lay has geared his text more towards applied mathematics than pure math anyways. I was able to learn most of the material on my own as my professor (as in most math and science classes) was really bad.

In summary, I feel that this book is good for self-study or as a saving grace from a poor professor.

I'm familiar with three linear algebra textbooks: Gilbert Strang's Linear Algebra and Its Applications, Georgi E. Shilov's Linear Algebra, and now this one. It was recommended to me by one of my brothers, who had the author as a professor at the University of Maryland - College Park.

Gil Strang's book is very well regarded, and I like it, too. However, as a writer, Strang tries a little too hard to be friendly and colloquial. As a result, some of his explanations are less clear than they need to be. It helps that videos of his linear algebra lectures are on the Web at [...], and those lectures clarify some of the "folksy" wording in the textbook. Strang obviously loves his subject and knows it thoroughly, but those qualities, however admirable, do not substitute for clear writing.

Georgi E. Shilov's book is also highly regarded, by me as well. Shilov is one of those no-nonsense Russian mathematicians who's all about the subject and doesn't care if you like him or not. As a result, his writing is very clear and straightforward, albeit a little stiff and formal even in translation. The great virtues of Shilov's book are that the writing is clear and it's very rigorous: in fact, a reader would do well to have some familiarity with abstract algebra before starting it. But the book's virtues are also its weakness: because of the rigorous treatment, Shilov offers considerably less conceptual hand-holding than Strang. Yes, you can understand what he's talking about, but you'd sure better have a strong mathematical background, time, and self-confidence to plow through his book, especially if it's on your own.

Which brings us, finally, to the Lay book. I am delighted to report that Lay combines the informal, encouraging tone and conceptual hand-holding of the Strang book with the clarity of the Shilov book. In other words, they're all good, but for most undergraduates, Lay is the best of the three. There's also an excellent study guide (Linear Algebra and Its Applications: Study Guide (update))for the Lay book.

I have heard students complain about how unhelpful this book is and professors complain that it is too easy.
I strongly disagree with both.

I am very well acquainted with the following introductory texts: Strang, O'Nan, Leon, Larson and Lay. As a student, I learned initially from the O'Nan text, then transferred colleges and had to repeat the class with the Strang text. As a professor, I have taught out of the 3 remaining texts. I have also examined the text written by Kolman.

Lay's Ch. 1 is an extraordinary result: he creates an overview that unites all the main ideas that comprise linear algebra.
No other text I know of comes near the breadth or clarity he achieves in this opening chapter. This chapter alone makes the book worth owning.

I also want to answer those who attack the Student Study Guide. It one of the few I have seen that is actually written by the author. It is likewise excellent and provides answers and hints for all the most critical problems in the text. I highly recommend it as well. I require it when I teach using the Lay text.

I have convincingly achieved my best classroom outcomes using the Lay text. I have actually covered most of the first 6 chapters and the first 2 sections of Ch. 7 at the junior college level in one semester with a decent group of students who were often slowed down by a group of underachievers in the class.

In summary, students who do not like this book will be hard pressed to find anything better- just pick up one of the competing texts used in colleges today and try to read it. Lay is by far the most 'user-friendly' text, he is clearly attempting to engage his readers. Unfortunately, most students at this level do not have enough experience at this point to make an informed judgement about the quality of a mathematics text or the quality of a mathematics teacher.

Professors who do not appreciate this text are an even more puzzling group. I can only surmise that the teachers in this group do not understand the ideas or the focus of an introductory class in linear algebra very well and are simply teaching without thinking.

1) My Background: I am an operations research analyst and have done some publishing of my own.

2) The Flow of the Book: The first chapter is fairly straight forward. This is true into about the middle of the second chapter. However, once Lay has gone beyond row operations, his clarity drops off dramatically. While the chapters follow a natural flow of a linear algebra class, the sections in the chapter are written in obfuscating language. It appears as if Lay is trying to show everyone how much he understands the deep abstract concepts of each Linear Algebra section; however, he doesn't really concern himself with explaining how he got there to the reader. In fact, he is down right condescending, stating that concepts, or lemmas are easily derived or deduced (which they very well may not be to most students; I sure did have a problem following many of his thoughts). The flow is purely terrible and is analogous to the spaghetti programming of the 70s and 80s with "as you recall from section x.x" being analogous to "goto" statements.

3) Errors in the Book: This book is riddled with so many errors that a professor at my community college offered additional points to those who could point out as many of them as possible. I can imagine nothing more frustrating than feeling that you have understood the concept and arriving at a different answer than the book, working it for hours, still not arriving at the same answer and then finding out in class that the book was incorrect. What an absolute waste of time. The editors should recuse themselves.

4) The study guide: Absolutely atrocious. Very few explanations, and those that are explained, leave out lemmas which may seem "easy" to the author, but are a stretch for the "introductory" student. This lack of explanation from Lay demonstrates sheer laziness and a lack of respect for the circumstance of the vast majority of his readers. Furthermore, giving true-false questions, but refusing to provide the correct answer prevents the student from being able to check his/her work, and more importantly, his or her reasoning. The fact that Lay does not provide comprehensive "reason" in any of his study guide exercise explanations compounds the ineffectiveness and lack of reasoning in the book.

This book is truly terrible, and it lives up to being the worst book ever. If you are looking for a clear understanding of Linear Algebra, ignore this book, and by no means should you purchase the study guide. You would do much better to go on YouTube, type in "Linear Algebra" and take MIT's tutorials. I am appalled by the lack of professionalism.

This book is an overview of Linear Algebra rather than a comprehensive study. The problems that really dwell deep into the concepts are left unanswered even when the problem is odd. You go to the back of the book and the answer isn't there; instead, it tells you to go to the STUDY GUIDE for the answer. Here's the clincher. You buy a $30 study guide, and then you flip to the correct section and the ANSWER ISN'T THERE. This is a BAD SALES SCHEME. The author claims that giving students answers inhibits critical thinking, but it's clear that he really intends for unwary students to buy his study guide so he can get money without exerting minimum mental effort. I strongly discourage people from buying this book. You'd be better off asking for help on the internet blogs.

I've used this book for two university classes. The book covers the material conceptually well, but the exercises are written as though you've masted the material before doing any exercises: basic theorems introduced in the book are not covered in simple exercises, and a high understanding is required to answer even some of the early exercises.

The study guide/answers solution guide is not terribly helpful, often giving answers without showing the needed work to get there (often the only reason you're reaching for the study guide in the first place).

If you have a choice between two classes, one which uses this book and another which doesn't, take the other class: avoid this book. If you just want to learn linear algebra, there's much better books out there. Avoid this book. Go with another book that doesn't have majorly negative reviews.

I wanted to give this book four and half stars but I cannot do that so I just rounded up. When I first started trying to learn Linear Algebra on my own, I was a little lost. After having enrolled in the course at my college, coupled with reading this book, I have a better understanding of it now. I am not a math major so I have no use for proofs and theorems. You may here others complain that this book does not offer any of that, this book, I believe, was designed for those other than math majors. Math professors can teach you the proofs and theorems if you need those, but this book focuses on other aspects, hence the title...and Its Applications.

Lay, lays out each chapter in several subsections that cover a wide variety of topics. Each example he gives is helpful to some extent, this is why I wanted to give him 4.5 stars, but not completely. However, Lay provides a wealth of resources through his web site, which well makes up for anything missing from his book. The companion web site offers several programs for downloading, I believe free of charge. These programs are available for MATLAB, Mathematica, Maple and the TI calculators. It also has other student resources as well. In addition to the web site, there is an included cd that provides detailed solutions to every third problem in the book.

Overall, this is a very good book that allows the student to easily comprehend the world of linear algebra.

underwhelmed
i'm not going to write 3 paragraphs about how much i love math, and what my fricking sat score was and how many A's i have as most nerds do when they review a math book. i am a math nerd too, but i'll keep the discussion to why i dislike the book (which will be short too, as i need to get back to studying it!)

1. i found there to be a nagging disconnect between the material covered and the exercises. i don't mind difficult problems, but at least appreciate some help from text. if i just wanted to figure it all out on my own i wouldn't have bought the book.

2. the study guide is not very useful. it provides solutions to every other odd problem. true / false answers just refer you back to the book and tell you to check your answers.

3. the text's answers to true/false problems tell you to think about it, then consult the study guide. see 2 above.

basically, i enjoy the material, my prof is great, the book is a big disappointment. if it wasn't for my prof's enthusiasm for the subject i'd be frustrated and not select any additional linear algebra electives. luckily, i do look forward to additional courses as the material is extremely useful in industry, i'm an applied math person.

finally, i searched for another text to supplement my studies and settled on Matrix Analysis and Applied Linear Algebra by Meyer, and look forward to its arrival. my second choice was: Linear Algebra : A Modern Introduction (with CD-ROM) by Poole, and it was a close second. both texts are highly recommended and very focused on applied subject matter. both have well developed websites, ect... but Meyer's text was published by SIAM with a stong focus on how the material is being used in practice. it also comes with a searchable, printable version of the text (and possibly study guide) on the cd.

if you want a balanced view before you buy this text. go to the 3rd ed, not the 3rd ed updated, and read some of the negative reviews in addition to the good ones. my experience was similar to many of those negagive reviews. disappointment and frustration with a very popular text. good luck.

Updated? I don't think so
In my opinion, this borders on the outrageous. I don't know if it is the author or the publisher, but someone should be ashamed to be taking such advantage of students. like shooting fish in a barrel and calling yourself a great marksman.

What is updated about this text? In my understanding, nothing! Update apparently means new chapters have been added to the publisher's website. most instructor's don't seem to know of this, so they don't use them, and they unwittingly order the newest edition. most students don't know either and needlessly fork over $120 for nothing new.

With vulture marketing practices like this I can't imagine why students would buy international texts.

if you are required to buy this text, check if you prof plans to use the "updated" chapters. if not, save some $ and go find a 3rd edition to use for your class.

good luck

I picked up this book because I wanted to review linear algebra that I studied years ago. This book has so many holes in the instruction that I could not recall what I learned years ago. The answers in the back of the text were of no help. The study guide was even worse. It would warn me to be careful but not tell me more. It would tell me to re-read a certain paragraph instead of giving me a solution. But the worst part, it does not even have the all the answers. If the author felt you should be able to figure out the answer on your own, he did not put the solution in. A solution manual with only selected odd problems is worthless. The author seems deceitful (bordering on dishonest) to sell the solution manual as such; it doesn't cover anything over and above the text book. If you have a choice, choose a different author for your text book.

For those of you who plan to find a self-study material, do not count on this book. I'm a PhD in computer science department and I'm looking for some books to brush my understanding about the linear algebra. I'm looking for "notions" instead of "derivations". The author does a good job in the first few chapters but I quickly lost after the vector space. I believe that I have some background, though not solid, in linear algebra, but the writing is so dry that I cannot easily follow the flow. I do believe that the author is very knowledgeable. However, as a self-study material, it would be too tough in my opinion.

If you are looking for a self-study book that is easy to follow (especially for deep topics). Be prepare that understanding the intuition behind the formula is not well addressed in this book. I won't say it's a 1 star book in the view points of quality. But apparently, you learn nothing if you cannot follow it, right?