ISBN0961408898

As someone who already knows the basics of the subject, I guess I'm looking at things with the benefit of hindsight. However, I needed to shore up my own knowledge of Linear Algebra and thought I might as well turn to Strang for a refresher and a different approach.

The result is that I am truly pleased with this book. His writing is lively and engaging. Linear Algebra has a phenomenal tendency to get dry and Strang does an excellent job of turning the subject this way and that so that one can admire it from every angle. In particular, there are three major approaches in this book that make it stand out.

1. Strang places heavy emphasis on vectors, vector spaces and transformations. This is good preparation for future study in Linear Algebra. This will provide an intuitive understanding of linear operators on vector spaces later.

2. Another reviewer mentioned that the book utilises a discovery-based approach. While this might be a disadvantage when you're in a hurry, the approach prepares one well for learning more theoretically oriented subjects where self-guided discovery is imperative. In this sense, I think the discovery approach is far superior to others and prepares the reader well for future studies. The problems are really fun (although I personally think they are much too easy). Many of the questions require light-weight proofs without undue formalism (not really required at this level). These pseudo-proofs really do help build understanding of the subject. Maths-phobes will not even realise that they're fleshing out the subject themselves.

3. The didactic approach taken in the book is conversational and informal. When added to the freely available video lectures at the OCW site, given by Strang himself, you really have a perfect introduction to the subject of Linear Algebra. The lectures are superb and Strang is an excellent teacher. His enthusiasm and passion for the subject is obvious and infectious.

I really wish I had learned Linear Algebra from this book initially. The book does a good job of encouraging geometric intuition and visualisation. That said, I do not think the book is an ideal book for maths majors. The primary problems being too little exposure to abstraction and problems which are too easy. However, I do believe that the book can be used in conjunction with a more rigorous approach in cases where the latter gets just a touch too dry. There is time to develop the rigour in theoretical Algebra courses at a later stage, with the added benefit that the reader will have learned the experimental approach to learning taken in the book.

I suppose some will find Strang's excitement over Linear Algebra a bit of a pain, but personally I think this conveys the sheer joy of pursuing an intellectual endeavour. I've always bordered on disinterest with Linear Algebra and this has been very much dispelled. I like to be reminded why I chose to study mathematics in the first place sometimes. While I can see that this book isn't for everyone, I really enjoy it and recommend it highly.

People say that mathematical truths never change, and that's true enough. New concepts, applications, and techniques keep emerging, though, so math teaching needs to keep up with the times. Strang has done an outstanding job of keeping this book current and relevant.

It's not a mathematician's math book - this is aimed at people who need results and needs computational techniques more than they need crystalline theorems. That's why it's so helpful to see applications like Markov models, Kirchoff's laws, and Google's analyses of the web. It's also helpful to see examples worked in Mathematica and MATLAB, the tools of choice for desktop exploration of numerical systems. It's startlingly easy to come up with a 100x100 system of equations, and just nuts to try to solve it by hand.

Strang assumes some amount of calculus in this book, something that other books on linear algebra sometimes skip. That raises the bar for the readership, but also opens up topics like change-of-basis in function space, including Fourier analysis. It also allows differential equations to be addressed as linear systems. Even without calculus, though, a reader is exposed to the singular value decompostion, QR and other matrix decompositions, and considerations in performing the computations. I found a few oddities, such as the description of a matrix's condition number. That has great physical meaning when it's taken as the ratio of the matrix's highest and lowest eigenvalues, but Strang gives a definition that I found less intuitive.

Such oddities are rare, though. Even though this book covers many topics, its emphasis is on clear and applicable presentation. I recommend this to anyone studying linear algebra or who, like me, has to brush up on basics not used in many years.

//wiredweird

I'm not one to be picky about an author's style of writing, but in the case of this book I have to be. It is COMPLETELY FALSE to call this book "introduction to linear algebra", what the title should be is "Gilbert Strang's ideas about linear algebra that no undergraduate in a first course in linear algebra will ever understand". Talk about inconsiderate instead of clearly explaining the steps involved in solving a problem, Strang will simple talk about some example of his personal interest that does nothing to solidify the main idea within the problem. How about the worked examples, he picks some arbitrary matrices and makes it so they can be solved in a single or very few steps that helps a lot when you want to know what's going on within the examples. Homework its freaking great to, the first question within each section is easy and than the second question and beyond is some kind of proof that you have no clue how to even approach because the author assumes you mastered the simple part in one question. I guess when you're a professor at MIT than you're automatically given the right to write terrible textbooks.

It's hard to rate the textbook by itself, because I'm also watching the videos of the author's class on the MIT Open Courseware website. But no doubt, the two of these together are an unbeatable combination. The website videos are excellent. I do find the book somewhat hard to follow when I try to read it before watching the videos, but afterward, it's quite clear. So maybe I'd rate the book a 3 by itself, but a 5+ in combination with the FREE online videos. Strang is an outstanding lecturer.

Gilbert Strang is a wonderful old professor who teaches Linear Algebra at MIT. He is also a terrible math book author. Written, well, like a brilliant man who is dumbing down his ideas for students, the text winds through multiple topics without ever nailing down important specifics. Even the chapter reviews, the 'concise points' of each chapter, are incredibly vague and nonspecific. For example, while discussing LU decompositions, Strang continually speaks of its computational efficiency but never mentions WHY the LU decomposition is computationally advantageous.

The book skimps even a bit too much on theorems, leaving you to believe Strang's hand-waving without walking you through the proofs. I understand this book is about application, but it's a bit too vague just to use for application; I don't need to know how you got to a proof, but I'd like to know why things in a formula works.

Maybe this book is better if you simultaneously take Strang's OpenCourseware class online. However, as a stand alone textbook, it's terrible. I've resorted to using Strang's chapter titles as my online search outline.