Introduction to Linear Algebra, Second Edition

Rating:
Summary: Exactly what is needed
Review: Dr. Strang's book is, hands down, the best introductory Linear Algebra text on the planet. Other reviewers complain about the "discovery" approach and the conversational style; in my view, these are strengths not flaws.

First of all, we have lost our way with modern mathematics texts by all but eliminating the idea of discovery. Nothing can strengthen the learning and understanding of mathematical material more than having to "find out for yourself" what is going on. Absent that process, one can only reach a superficial understanding of the topic at best.

Second, it's refreshing to see a truly conversational approach. Once again, there are too many dry definition-theorem-proof texts out there ... they're maybe appropriate for a more advanced exposition, not for an introduction.

In many ways I agree with Dr. Strang that we teach too much calculus and not enough linear algebra. The former has been the standard sequence for undergraduate mathematics for years; nifty stuff but seldom, if ever, seen outside the classroom. Linear algebra, on the other hand, is alive and well in industry and just may be the most useful set of mathematical tools available to the technical types.

Everone studying or using linear algebra would find time spent with Dr. Strang's book an excellent time investment.

And for those not liking discovery or conversation, maybe you should try a different course of study ... you've missed the boat on this one!!

Rating:
Summary: Teach the subject to the non-math students
Review: Gilbert Strang is a very experienced teacher of Linear Algebra, and this book is written as a text to his MIT linear algebra class. Math majors will not find the 'definition-proposition-lemma-theorem-proof-corollary' treatment here, instead Strang, aware of the need to teach non-math majors the subject -- explains linear algebra in a simple but effective way = examples, diagrams, motivations, etc. This book is one of those that you can use to skip class the whole semester and get good grades with (but don't do it! get your education in the classroom).

Rating:
Summary: Excellent book if you are academically mature
Review: I agree with most of the reviewers that this introduction to linear algebra comes at an advanced level and an advanced pace, but I disagree that it's not a good introductory book.

If you are academically mature and you have a bit of patience, you will find that this book is much better than other introductory books. It gets much deeper into the heart of linear algebra more quickly than other books. When reading a math text, it's important to re-read and re-think each idea. If you don't do that here, you will miss the great wisdom that Strang (author) has masterfully woven in a genuine and caring tone.

Rating:
Summary: basically a good math book
Review: I give this book 3 stars mostly because of Strang's style of writing and not so much for the information contained in the book. The lucid prose and the overabundance of exclamation points in the text (you'll see what I mean if you buy it) make this book read as if you were talking to a really cool math professor who knows what he is talking about and is excited (oh yeah) about linear algebra. That part of the book is great, but this book definitely does not cut it as a reference book. When I took linear algebra years ago, I thought the book had lots of really cool things in it, but now, when I need to look up some advanced linear algebra topic for another advanced math class, I simply cannot find anything useful in this book. If you are considering buying this book to supplement your library, be warned that it is a very basic treatment. Also, this book places less emphasis on applications and computations, so non-math majors may not find it very helpful.

Rating:
Summary: Strang's books
Review: I learned linear algebra from an earlier edition of
Strang's book many years ago at MIT and it has only
gotten better. I thought then and still think that the
presentation is excellent and the main ideas are
extraordinarily accessible-- it is not the
theorem:proof presentation typical of many advanced
mathematics texts which can obscure the underlying
structure for folks not intent on becoming mathematicians
(and perhaps even some budding mathematicians too).

Now that said, it might be too wordy for a reference text
and perhaps could use a quick reference guide something
akin that seen in introductory books on other topics
(the LaTeX book by Lamport or Ritchie's C book). However,
a better go would be to simply use Strang to LEARN the
material and then any of a variety of reference books
collaterally (kind of like using Yates and Goodman for
learning probability, but Papoulis or Feller for a reference).

Rating:
Summary: Strang's books
Review: I learned linear algebra from an earlier edition of
Strang's book many years ago at MIT and it has only
gotten better. I thought then and still think that the
presentation is excellent and the main ideas are
extraordinarily accessible-- it is not the
theorem:proof presentation typical of many advanced
mathematics texts which can obscure the underlying
structure for folks not intent on becoming mathematicians
(and perhaps even some budding mathematicians too).

Now that said, it might be too wordy for a reference text
and perhaps could use a quick reference guide something
akin that seen in introductory books on other topics
(the LaTeX book by Lamport or Ritchie's C book). However,
a better go would be to simply use Strang to LEARN the
material and then any of a variety of reference books
collaterally (kind of like using Yates and Goodman for
learning probability, but Papoulis or Feller for a reference).

Rating:
Summary: A great book for self-study
Review: I used the book for self-study in combination with Strang's freely available video lectures. The book's emphasis is on understanding and appreciating concepts, rather than on formal proofs. As I have experienced him, Strang is very good at explaining things. He uses lots of examples, and, the textbook as well as the video lectures are very easy to comprehend. His informal writing helps to make the book an interesting read. For me, having had some linear algebra in high school, most ideas were familiar. However, it was always delightful for me to look at Strang's perspective on things. One clearly sees that Strang has a lot of experience in teaching linear algebra. He introduces new ideas in a very natural way, emphasizing what they are good for beforehand. I particularly liked the chapter on determinants.

The book doesn't require any prior knowledge besides very basic high school math. I used it in my year of civilian national service, before starting to go to college. Compared to other college level books for math majors I have looked at, this book works great for self-study. The level of difficulty seems to be something inbetween high school and university level (math major).

Rating:
Summary: How not to write an introduction to linear algebra
Review: I'm still wondering why my math department chose to use this book for the first course in matrix algebra. There aren't very many examples, and also, there aren't very many geometric representations (pictures) to help the students who have trouble visualizing things (after all it is only an introduction where not all of the students are going to be carrying on in math). More than half the class complained about these things. After going through the book 2 terms later, I don't think it's a total piece of garbage. I could understand how someone who hasn't seen the material in a while would like it. It would be useful to jog someones memory, and a lot of the problems are really interesting (like making a magic matrix and multiplying it by (1,1,1,..,1)), but it's not so good as a first look at linear algebra.

Rating:
Summary: Borrowed 4 times from library; time to buy.
Review: This engineer is interested in the insight that maths can provide, not the proofs that can be written. This book aims for insight.

If you want to put the students to sleep, if you don't want your class to see past the proof then this is not the book for you.

Rating:
Summary: too conversational
Review: With only two days from my final exam in Linear Algebra, I figured it's a good time to review this text, briefly. I really like the author. I enjoyed watching the video lectures at the MIT website associated with this book, given by the author himself. The problem is that he doesn't explain the topics as clearly in the text as he does in his lectures. There is entirely too much emphasis on the "discovery" approach. Instead of just clearly explaining many of the important subjects like Determinants and Eigenvalues/Eigenvectors, he chooses to leave the student in the dark to "discover' these for himself or herself. I don't mind this method in small doses. However, it ends up being a frustrating experience when trying to do homework assignments. He dips into the abstract without warning, draws many conclusions that require one to read the sections over and over again, trying to grasp the concept. In future editions, I would recommend removing some of these more difficult concepts from the problem sets and, instead, placing them into the text where they really belong.
As a final example, I would appreciate it if Dr. Strang would link-up the concepts of Column Space, Nullspace, etc to Orthogonals to Eigenvalues/Eigenvectors in some way....How about a two or three page sidebar that ties them together. This would have made the subject much clearer than it is in this edition.