Linear Algebra with Applications, 5th Edition

I absolutely love this textbook, I used it for my linear algebra course at UCLA and it was such a good resource, not only for finding all the formulas but also in explaining the conceptual aspects of each topic. It also connected the topics very well and flows very seamlessly if you read it from front to back. I highly recommend this textbook!

It gives you frustration when you hope to get homework done in one hour with this book. You would read page after page without getting the quick answers you are looking for.It gives you fulfillment when you relax and read this book from beginning. This book explains concepts in depth and stimulates thoughts. It provides adequate examples and background information before revealing main ideas, so you can actually figure out the main ideas on your own. Then, read the printed theorem on the next page --- the exact thing you've been thinking! It feels so natural to DEVELOP linear algebra! BTW, this book also explained the connection among topics pretty well.In sum, great textbook to understand math; not a good source to find quick answers. I recommend spending 3-5 hours per week on this book to learn linear algebra in one semester. Use google when you are in a hurry!

I'm not sure how many of these reviews you see have been written by (potential) math majors, but I can assure you that their say is underrepresented. Many of the complaints I rad here reflect what many of my classmates have said. That the explanations are not complete, the problems at the end of each chapter don't correspond with examples in the text, etc. etc.Well, folks, that was kind of the point. It's not supposed to be plug-in-chug, nor is it meant to be easy. You are not supposed to know 'exactly' how to do the problems at the end of each chapter once you read it once. No, you should read it again. Then try the problems. Then read the chapter again when you get stuck. That's the point. You are supposed to think. And I can assure you, nothing beyond elementary algebra and very (very) basic calculus background is assumed. All of the problems are eminently doable. The trick is just realizing how easy they are. But until you realize that, it's very hard. And that's pretty much what learning math is all about.I'm only a rising sophomore, so I still have a long way to go before I can make any claim that I understand this material fully, but having seen what a more dense mathematical text looks like I can assure you that this book is a wonderful thing. Don't take the pictures and diagrams for granted. Embrace them. Everything in this book is here to help you. Do as many of the problems at the end of each chapter as you can. Often they will want you to prove something that will be proved in the following section. This is important also. Even if you don't get the answer right away, the point is to try and see how far you can get. Once you read the proof they do go back and try it again. You'll be amazed how much more you understand.My only criticism of this book concerns the very beginning of it. I thought these reviewers were right. Everything felt unclear and muddled and I was very confused. I was angry at my professor for using this damn book. But if you carry on and march through chapter three, things begin to pick up. You will see the light at the end of the tunnel. I think this has to do a certain level of abstraction that Bretscher avoids in the beginning, which makes things unclear at times. When you talk about reduced-row echelon form, you will take a lot of things for granted. Things will always sort of make sense. Eventually, things just make sense (I promise), but you will have to bear with the first few sections first. This is just the nature of the "with Applications" part of the title, I believe. It's meant to ground you somewhere comfortable (i.e., someplace with numbers, because this course could certainly be taught with numbers!).So, to summarize- try to have fun with this book! I'm certain you can.

I used this book for my linear algebra course at Harvard. The authors did a really good job at making it accessible to people coming from different backgrounds without sacrificing rigor or conciseness.

I go to a small competitive liberal arts school with a lot of serious math students, where this book is renowned for being horrendous. No one's quite sure why all the professors still use it - maybe one of them is friends with the author - but I've never heard a student defend or compliment it.The text focuses on phrasing ideas as pedantically and densely as possible, without discussing the significance or logic behind them. Occasionally, an example use or higher-level rationalization is given, but typically the chapters are just a jungle of definitions and proofs by algebraic simplification or induction.I'm no stranger to theoretical math or mathematical notation, and neither are many of my peers. However, this book makes absolutely no attempt to tell you *why* anything it contains is profound, let alone worthwhile. It spends a long time, for example, proving and discussing very specific and painfully boring shortcuts to computing determinants. While that may become useful when implementing some high-performance matrix processing library, I can't imagine it's a valuable use of time in an introductory undergraduate course. Meanwhile, far more interesting and significant, and sufficiently pure topics like PageRank are only briefly glossed over in "optional" pages at the end of some sections. Maybe I'm just not brilliant enough to tap inspiration from the plodding definitions and parlor-trick equations the book methodically and painstakingly feeds you, but I suspect otherwise.It seems that this book, like most calculus textbooks, has confused "interesting" with "pedestrian" and "useful" with "applied". In doing so, it attempts to make things hard simply by drowning you in technical language, vagueness, and memorization of rather arbitrary techniques, like those for finding determinants or certain forms of eigenvectors. Unlike a harder and more notation-focused discrete math course I took, I came out of the linear algebra course that used this textbook feeling that I learned nothing interesting about how the world works, and nothing that I might use in any future intellectual pursuit. It was, aside from Chapter 1 (which I had already learned in discrete math), a waste of time.

The only problem with it being an use book is the pages were kind of ripped from the hard cover, but I received the book in a timely fashion, it serves its purpose and I am doing great in the class so far.