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Rating: 
Summary: Great Book, Great Problems (Hints - Give away)
Review: I bought this book to supplement Strang's Linear Algebra and its Applications and wound up switching over to this book. Good coverage of important topics. Concentrates on giving the reader some geometrical insight which might turn off some but which I personally liked.
About 4 sections per Chapter. Each section has 50 problems. A lot of them are number substitution or fact manipulation. A few of them are really "nice" problems. However the author gives away the entire solution in his "hints". He should have put them at the end of the book. So if you want a challenge avoid the hints.
Overall a great book.
Rating: 
Summary: Pretty Bad....
Review: I have taken many math classes in my career (I am currently a graduate student in statistics) and I would have to say this is one of the worst texbooks for introductory linear algebra out there. This book was assigned in an introductory linear algebra course at Cornell and if it weren't for other, much better linear algebra books, I would not have done well at all. One of the main flaws with this book is the lack of concrete examples, which in itself is enough to make it a terrible introductory text, but in addition, the study guide ironically gives detailed answers to relatively easy questions but NO explanation AT ALL of difficult, more theoretical exercises. The only reason that I can figure as to why this book is so popular among good universities is that they are trying to give students a hard time early on, perhaps to discourage them from taking further mathematics courses. I feel great pity for those that have the misfortune of being taught linear algebra with this book.
Rating:
Summary: Difficult and Too Concise
Review: I pretty much read this entire book front to back. It covers most basic linear algebra concepts. I don't understand why this book is getting such a poor review. It's concise and to the point. It's mathematically accurate and the problems can be challenging. The notation can take a while to get used to but it is mathematical convention. I found the part on fourier series to be very useful for studying more advanced math topics and for engineering.
Rating: 
Summary: Great Book
Review: I really don't understand what all the moaning and groaning about this book is. I had it in my introductory linear algebra class, and although the book requires a great deal of independent work and thinking, that is certainly what math courses in college should emphasize. I appreciated the fact that the book set out a theoretical concept and required the student to "apply" the concept in the excersises. Through this approach, the student gets a lot of satisfaction in finally being able to tie concepts together, and seeing how all of linear algebra fits together.
If you want an easy text that will not make you think and understand concepts fully, than this textbook is not for you. However, if you want to really understand the theory behind linear algebra, I totally recommend this book. In particular, the true/false questions at the end of every chapter really tie everything together and synthesize the theory with actual computations quite well.
Also, I thought that this book was much clearer than the Strang book, but that might just be me.
Rating:
Summary: The WORST
Review: I used this book for an undergrad Linear Algrebra class. I found no great faults with it, although it is somewhat sparse and only explains most topics in one way. I found it more than adequate for the class, although I did supplement it with free material off the web including Dr. Strang's Linear Algebra notes.I wish that the problems had been more difficult, and that Mr. Bretscher had put in more footnotes explaining equivalent terminology to what he uses (eg. explain what row and column spaces mean, since that's used a lot elsewhere). Also, some of the proofs are a little bit incomplete. There are many times where he depends on you having worked-out solutions to previous homework problems, which is easier for the author, but hard for a student trying to follow the logic.
Rating:
Summary: This is the worst book ever written by man
Review: I was required to purchase this book for a course called Linear Algebra with applications. This book seems to just cut out important theorems, proofs and other pieces of explanation commonly found in other text books I have looked through, and rather than making up for it with a decent explanation or summary for what it omits, it leaves gaping holes in many topics. It gives partial proofs and explanations at times and leaves other pieces "for you to solve as exercises." It's like the [person] who made this book only wrote half a math book, and left the other half for you to figure out in problems at the end of the chapter. Additionally, some of the diagrams are often, but not always obvious, unneeded, or on the other extreme confusing.... If you are forced to get this book then do not go without the supplementary answer guide (sold separately, unfortunately like most) because there are several problems that are completely wrong or misprinted answers in the answer key at the back of the book and only corrected in the answer guide. Oh, and the website, as of last week, doesn't work (I've tried it on several computers). The plugin, (I think it's called LiveMath) that is required has changed versions (been updated) and none of the online examples have been made to work with the latest version of the plugin. So this, added to the fact that the website sucks anyway, makes this book totally worthless. (try the website, maybe it has improved: www.prenhall.com/bretscher). If you can afford it, buy a real Linear Algebra book while you are at it. (there are also some good ones online you can download as *.pdf's) Otto Bretscher should go to jail for this crime of a math book.
Colby College should be ashamed to have its name written in this book.
Rating:
Summary: Difficult and Too Concise
Review: I've never had such a hard time in a math class. I realized quickly that linear algebra is completely different from the mechanical things I've been learning. This subject is very different and very abstract. I knew I really had to STUDY and not just read this book. Considering all of this, when I picked this book up, I was apprenhensive from the start. Whenever I see a thin book assigned for a subject that's entirely unfamiliar to students, I know it's going to be a very concise book without many examples and detailed explanations. The few people who have given this book rave reviews sound like instructors. If you are an instructor reading this review, please keep one thing in mind: textbooks are written for students, not you. What difference does it make if you think it's great but your students can't understand the most basic concepts, which was happening in my class? Yes, this book will make you think--think for hours on such basic concepts as what's the difference between a rotation and reflection. One more example of a linear transformation would've made all the difference in the world. The very first exercises will often leave most students saying, huh? Thinking is great but if you have to search the web and buy other books to get more information, that book is worthless. I'm a computer science major and there are books I really think are well-written but I would never recommend them to someone who's never touched the subject. I believe if most of the students don't like it, there's something wrong with the book (many of my classmates complained about this book as well). If you are a math major or someone with a PhD, of course, a concise and clean explanation is great. But for students who've never had it, it's a nightmare. It's a situation I see too often: the textbooks that are assigned usually get the worst reviews yet they keep getting assigned again and again. This is especially true in science and math courses.
Rating:
Summary: For me, the conciseness was a plus!
Review: It looks like some of the reviewers here disagree with me, but I think this textbook is excellent. The explanations and examples are generally very clear, and there isn't a lot of distracting nonsense. In many textbooks they try too hard to teach through "Real World" examples. i find such examples confusing because they obscure the math behind the example. I also felt this book had a nice mix of easy, medium and challenging problems. And it feels like the author really understands and strives to clarify many of the hurdles faced by Linear Algebra students. Make no mistake about it, Linear Algebra is a tough class that requires a lot of dilligence and abstract thinking. This book isn't going to guarantee you an A. But if you work through it, and if you have a helpful teacher, you'll be on the right track. By the way, I am a Computer Science major, and while I consider myself decent at math, I'm by no means a math genius. :)
Rating:
Summary: For me, the conciseness was a plus!
Review: It looks like some of the reviewers here disagree with me, but I think this textbook is excellent. The explanations and examples are generally very clear, and there isn't a lot of distracting nonsense. In many textbooks they try too hard to teach through "Real World" examples. i find such examples confusing because they obscure the math behind the example. I also felt this book had a nice mix of easy, medium and challenging problems. And it feels like the author really understands and strives to clarify many of the hurdles faced by Linear Algebra students. Make no mistake about it, Linear Algebra is a tough class that requires a lot of dilligence and abstract thinking. This book isn't going to guarantee you an A. But if you work through it, and if you have a helpful teacher, you'll be on the right track. By the way, I am a Computer Science major, and while I consider myself decent at math, I'm by no means a math genius. :)
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