Overall it is a mediocre math textbook with classic math textbook layout, theorem-proof-example, but the language it used is quite confusing. I mean, not pedantic that kind of confusing, but rather the interchanging of terminologies makes it hard to follow up. Linear algebra this subject has a huge amount of concepts that tell you the same thing from different perspectives and it requires a lot of work to be done by yourself so that you can absorb the concepts and convert from one to the other. Yet this book uses too often different terminologies, even in the same sentence, to explain a simple example without further explanation. So sometimes you need to look back and forth just to understand what he is talking about, which is frustrating. And most of the points are made between examples, without a clear definition before and after the them, which is kind of messy. The major complaint I have for this book is its lack of explanations. Most of the time it just tells you the exact procedure to solve a problem, like the way to perform LU matrix factorization, but fails to explain how to derive it from the knowledge mentioned before. And this book uses a really implicit way to point out the connection of chapters so sometimes when you look back several chapters you will find everything become clear. In addition, notations used in this book are HORRIBLE!! For instance, chapter 4.8 difference equation, if you study by yourself without your instructor's notes, you will completely get lost in its disastrous way of using notations. I cannot even figure out what is vector, what is sequence and what is scalar. This book adopts nontraditional way to organize the material. Instead of applying the knowledge after fully introducing them, this book first talks about really basic skills and then mixes the most advanced concepts and theorems with real world application and does not tell you how to relate them with previous chapter. Drawback of this approach is it definitely escalates the level of difficulty for students to learn them, but advantage is if you work really hard and once you understand the model, you will master the material. Another complaint I have about this book is it just tell you this is the model and how to solve it but not to mention how to set up the model...So whether this book is good or not, you can make the decision by your own.
Some advice to do better using this book:
1. fully understand all the basic concepts.
2. go through examples carefully and connect them with prior knowledge if you want to know why it is like that.
3. if you don't understand something just refer previous chapters you may find some clues.
Good luck to all of you!