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1 of 1 people found the following review helpful
5.0 out of 5 stars
An essential second course for mathematicians and physicists,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
Linear algebra is typically a course taught mostly to scientists and engineers who need to use the methods of undergraduate linear algebra to calculate things. To serve that need, and to avoid abstraction, the undergraduate linear algebra course teaches matrices, more matrices, and only matrices. Only years later do students discover that they can adapt those theorems about matrices to other situations. Often they do this quite carelessly, or if they are careful, avoid doing so and resort to more difficult methods. That is because they have not read this book. If every university had a class called "Linear Algebra Done Right", fewer math students would enter graduate school thinking that linear algebra is about matrices, and fewer otherwise sophisticated physics students would deal with linear operators by saying, "Dude, pretend it's a matrix!"
Intended to follow and complement that inescapable first class in linear algebra, "Linear Algebra Done Right" emphasizes the abstract over the concrete and elegance over brute force. Eigenvalues are banished to the latter half of the book and replaced with an abstract, definitiondriven development of the basic theory. Students are liberated from coordinate hell and introduced to beautiful and powerful concepts. That perspective is unnecessary and probably confusing for engineers and scientists who only need the matrix methods for calculation, but it is a natural approach for mathematicians, physicists, and others who need a deep understanding of linear algebra to support their attack on more advanced mathematics. A note on style: Although the material is introductory, the style is slightly more sophisticated than most introductory texts. To understand the material, the student must read closely, fill in the gaps "left as an exercise", and do the problems. This is the way all advanced mathematics books must be read, and "Linear Algebra Done Right" provides a gentle introduction to that manner of reading.
1 of 1 people found the following review helpful
3.0 out of 5 stars
A Nice Approach for Diehard Math fans,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
Sheldon Axler's "Linear Algebra Done Right" is an excellent book for the strong of heart. I am an undergraduate student majoring in mathematics, and my professors are obsessed with this book. I, however, am not.
First of all, there are no solutions to the exercises at the end of each chapter, so students are left frustrated when they cannot arrive at the next step of a proof. Second, what the author sees and deems "obvious" as far as steps and recollections are concerned is not necessarily obvious to the reader. Axler tries to motivate readers for the proofs by offering little exercises for them to "verify." That's overkill, but to many professors and analysts, overkill in the abstract is probably necessary in order to ensure a given student's success in an advanced linear algebra course. I'm taking one such course to fulfill my requirements for a math major, and must say these abstract/proof courses get very monotonous and, thus, ridiculously boring. The text, itself, for this book does not particularly motivate me, and I expect to consult the chapters to learn and understand concepts, not to verify info from the chaper. Essentially, the flow of the concepts is ruined by the lack of examples; how are we supposed to verify ideas when the author hasn't really even exemplified the components of them yet? I find myself falling asleep before I even complete one or two pages in this book. The layout is dull and the propositions and theorems seem endless. My point is the following: That which is good for the instructor is not necessarily good for the student. Students need motivation, and it is difficult to achieve this goal without offering students detailed examples, interestcatchers and solutions to the timeconsuming and overwhelming exercises and concepts. In the realm of the college curriculum, this book is average. I understand the difficulty of making abstract algebra interesting, but this notion is precisely what students need. To the student math geniuses and professors that live and breathe math, this book is a gift from the gods. To your average math student, however, that lacks patience and the desire to give up their free time to submerge himself/herself into this book, this book, like mine, will just end up sitting on the shelf and collecting dust.
1 of 1 people found the following review helpful
3.0 out of 5 stars
Good book for subject instructors, bad choice for students.,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
The text is preety terse and condense, it would be a delight if someone taking such courses from college and learned from an instructor. It would be a real bad problem if someone use the book for self study or as a reference material for more serious studies for no problems solutions were provided (this indirectly show the author definitely try to marketing the book to college instructors as teaching materials than as selfcontained study materials. As a graduate student, I would stronly recommend users to consider Strang's Linear Algebra and its Application for their first choice as the real world approcah to problems and also as a stepping stone to more advanced theoretical studies in linear algebra.
For instructors this is an excellent choice for text book in the market for the price of the book is affordable to most students and meanwhile most important concepts and materials were hiding in the problem examples which will definitely challenging the most capable students and will be easy to curve the course grade in tests and exams.
1 of 2 people found the following review helpful
2.0 out of 5 stars
good book for instructors, bad choice for serious students,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
The book is very terse, and most of the hightlights on the text is hiding on the problem examples, which only the instructors can either understand and access to it thoroughlly. I would recomd Strang's Linear Algebra and its application to most students who get a chance to know the hints of the problem and motivate them to more advance theoretical studies of the subject.
1 of 2 people found the following review helpful
1.0 out of 5 stars
It Should be Called "Linear Algebra Done Wrong",
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
In a word: horrible. The author takes a totally wrong approach to linear algebra. He introduces matrices towards the end of the book, and spends about a page on them. The book is written in an essay format, with very few examples and workedout problems. A better choice would be Bernard Kolman's Elementary Linear Algebra.
5.0 out of 5 stars
really really good book in linear algebra,
Verified Purchase(What's this?)
This review is from: Linear Algebra Done Right (Paperback)
This text is easy to understand, formulated quite generally (for example the author uses vector spaces defined over arbitrary fields, not just R or C), and contains lots of examples (possibly too many examples). I don't think I can overstate how good this textbook is. In conjunction with a good text on the computational/algorithmic aspects of matrices you would have a complete undergraduatelevel education in linear algebra. I know its a stupidly horrid title, but it is a really good book. The only con would be its shortness; I think there is a lot more room for other topics.
5.0 out of 5 stars
Elegant theoretical presentation of linear algebra,
By
This review is from: Linear Algebra Done Right (Paperback)
This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent. The student has perhaps taken a linear algebra course designed for engineers and scientists. Such a student is comfortable reading mathematics and writing proofs. It is meant to be read and reread until the ideas are absorbed. The exercises are relatively easy and no answers are provided. With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.
Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra. The price is right. This could be a very useful purchase even if it's not assigned as a text.
5.0 out of 5 stars
One of the best books on the subject.,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
As a graduate student in engineering at UC Berkeley, linear algebra is an essential tool for research and problem solving. I was lucky to take a linear algebra course taught from this book. This book is very concise, illustrative and very complete. None of the other popular books on linear algebra presents normedvector spaces and their operators or the proof of the Jordan canonical form as precise and rigorous as this book. I think that Prof. S. Axler (the author) who is UC berkeley graduate himself has done a great job to write this book.
5.0 out of 5 stars
Highley recommended book on abstract linear algebra!,
By A Customer
This review is from: Linear Algebra Done Right (Paperback)
This book is very well written and a pleasure to read. I used this book for my second linear algebra course. It was a wonderful account on finitedimensional vectorspaces and finitedimensional operators. Axler's approach of not using determinants is most efficient and very helpful to "see what's going on." This book isn't meant for those that want an applied course in linear algebra; only abstract material here! It's meant for junior/senior math majors who have some "math maturity." While Axler's very careful with the presentation, those with little experience with reading and writing proofs may find it challenging. If you're into math, pick it up and have fun!!!
5.0 out of 5 stars
Very good,
By Toan Vu Phan "Dostoevsky" (Northwestern U, IL USA)  See all my reviews
This review is from: Linear Algebra Done Right (Paperback)
An well written book with an elegant approach to linear algebra, by a famous author.
The book has good exercises, thou not very hard. I only wish Prof Axler had talked a little bit more about applied linear algebra. 
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Linear Algebra Done Right by Sheldon Axler (Paperback  April 6 2004)
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