Linear Algebra with Applications (3rd Edition)

KEY BENEFIT: This trusted reference offers an intellectually honest, thought-provoking, sound introduction to linear algebra. Enables readers to grasp the subject with a challenging, yet visually accessible approach that does not sacrifice mathematical integrity. Adds over 400 new exercises to the problem sets, ranging in difficulty from elementary to more challenging. Adds new historical problems taken from ancient Chinese, Indian, Arabic, and early European sources. Strengthens geometric and conceptual emphasis. A comprehensive, thorough reference for anyone who needs to brush up on their knowledge of linear algebra.

I also felt this book had a nice mix of easy, medium and challenging problems. And it feels like the author really understands and strives to clarify many of the hurdles faced by Linear Algebra students.

Make no mistake about it, Linear Algebra is a tough class that requires a lot of dilligence and abstract thinking. This book isn't going to guarantee you an A. But if you work through it, and if you have a helpful teacher, you'll be on the right track.

By the way, I am a Computer Science major, and while I consider myself decent at math, I'm by no means a math genius. :)


A great book for self-tutoring   June 2, 2006
John A. Papaioannou (Ithaca, NY)
8 out of 12 found this review helpful

I took an undergraduate course in linear algebra which assigned this textbook and basically, it made the lectures dispensable, it was that good.
The text is very well written and presents the concepts being discussed in a visual manner complete with many diagrams to aid the reader. A fresh surprise is that the author's personality really shines through in the text as he includes many side comments and interesting historical footnotes which really enrich the book. Every new concept/lemma presented is coupled with an example which I find to be extremely important.... and for further study the end of the chapter problems range from simple computational types to nail down various processes to much more abstract and proof oriented types which are very rewarding and insightful.
Now, this book was assigned to both the linear algebra course for math majors and the linear algebra course for engineers and it was my understanding that math majors preferred the text over the engineers. This is probably because it is a conceptual/theoretical treatment of the material and does not really contain too many applied math problems. It is only in the last few chapters regarding linear differential equations in which the book delves into mathematical physics where the applications are obvious.
Regardless, if you want a textbook to learn the fundamentals of linear algebra this is it.

EDIT: I forgot to mention that there's a whole section on data-fitting and least squares which is purely applied linear algebra... so there's a bit more applications than I remarked earlier.


A Contrarion Review   October 14, 2000
D. E. Orr (Vancouver, Washington United States)
6 out of 9 found this review helpful

Contrary to the other reviewers, I found the book to be outstanding! A possible reason for the different view is that I had studied linear algebra before. This books needs to be read and followed carefully and thoroughly- it is comprehensive and explains what is 'really going on' in the realm of linear algebra. Basic ideas, theorems and computational methods are presented with clear examples and pictures illustrating the geometry involved.

It is clearly not a 'cookbook' that one reads quickly to find the recipe for passing a course.


Nice intro to linear algebra   November 1, 2003
Alan Chen (United States)
5 out of 7 found this review helpful

I pretty much read this entire book front to back. It covers most basic linear algebra concepts. I don't understand why this book is getting such a poor review. It's concise and to the point. It's mathematically accurate and the problems can be challenging. The notation can take a while to get used to but it is mathematical convention. I found the part on fourier series to be very useful for studying more advanced math topics and for engineering.


Unlike most others here, I really liked this book   December 11, 2005
Solsa55 (Bay Area, CA)
3 out of 7 found this review helpful

I really liked the visual approach to this
topic. Can't begin to say how much this
gave me an intuition on how linear algebra
works. Much better than the formulas I
see in most math books. I have a terrible
memory for formulas but an excellent
memory for illustrations.

Of course, there are still theorems
and formulas, too. Anway, really liked
this book. I used this book a year
ago and still feel like I remember
all the major concepts and would be
able to recall any particular section
after a brief review (definely cannot
say that about many of the math classes
I have taken.)