ISBN0030105676

I've used the third edition in conjunction with Professor Strang's excellent video lectures on the MIT OCW site. The combination of the two is absolutely superb. If you do the exercises at the end of each section you will learn linear algebra even if you never intended to!

This is an excellent book for people who will work with linear algebra for the rest of their careers. For the typical linear algebra student it is also very valuable, although for them Strang takes too much pleasure in non-essential tricks of the trade. For example, elementary matrix theory is crowned by a discussion of "the four fundamental subspaces". This quartet is introduced as a triumphant theoretical unification and we then see them each play their part to the letter in a flawless staging of Kirchhoff's circuit laws. Although a stunning performance, it is a connoisseur's delight more than anything else. This is just one example of a beautiful application "tied up" in a lot of theory. As a second illustration, finding the n:th Fibonacci number (p. 256) can be done with just straightforward diagonalisation rather than difference equation theory. Strang's way if of course the best way, assuming that the reader has lots of time. Naturally there are also application that are very enjoyable in isolation, both nuggets (e.g., it takes as many operations to compute A^2 as it does to compute A^-1; p. 48) and entire sections (e.g., a good introduction to game theory, pp. 408-414). The fact that this book is written by a linear algebra user rather than a textbook author also has many other benefits besides the actual applications. To take but one example, it continues to puzzle us how so many linear algebra textbooks can fail to emphasise the interpretation of matrix multiplication in terms of linear combinations of columns (p. 23).

Strang tends to get all holier than thou and advocate the de-emphasis of calculus in the academic curiculum and replacing it with Linear Algebra. That's like advocating the replacement the de-emphasis of the Bible and replacing it with a text on the comparitive study of religions. Crazy.

Still, Strang is a pretty good teacher and writer. Just can't get over his craziness. Calculus is the foundation for differential equations and differential equations (ordinary, linear time invarian, vector as in Maxwell's, or what have you) are the foundation for science and technology. Linear Algebra can extend such a foundation, but it can't replace it.

I can understand Linear Algebra much better than say Partial Differential Equations, but that doesn't mean I think Linear Algebra is more important. It just means that Parital Differential Equations have more to them and should be taught more, not less.

My first complaint about this book is it is too expensive. But If your teacher follows it then go for it. If you have determined to master linear algebra and be able to spend time for the course videos the author gives then this book is worth buying it. No no if you want to just refresh some concepts because it's too expensive.

I was tired of seeing the theoretical based linear algebra books and so I decided to buy one that focused on applications as well. I got a used copy of the 3rd edition. It's really good on applications. I recommend this book highly for applied mathematicians, scientists and engineers. However, I found some of the applications a bit confusing and some of the problems assigned could be challenging. In my opinion, I think this book has about 35% - 40% theory and the rest applications. Buy this book if you really want to see the applications of linear algebra.

-Patrick.