Rating: 
Summary: Not bad...
Review: A pretty good textbook, but by no means outstanding. I learned a lot by working the problems. I did not, however, learn how to do more than simple proofs. Instead of outlining some methods as to how beginning students should go about learning how to prove theorems, the author assumes you already know how to do that. Consequently, I didn't master that skill. It also would have helped if the Solutions Manual that accompanies this text were available to students; maybe by now they've made it available. Leon definitely does not include enough worked examples in the text, and those problems where "The Proof is left as an exercise for the reader" are useless and defeating. I wholeheartedly disagree with the review above that "if you can't handle this text, don't major in math, you don't have what it takes". Nonsense. Provided you give it your all, you can major in math, and understand Leon's text, even if you aren't blessed with sheer, infallible intellect.
Rating:
Summary: Not bad...
Review: A pretty good textbook, but by no means outstanding. I learned a lot by working the problems. I did not, however, learn how to do more than simple proofs. Instead of outlining some methods as to how beginning students should go about learning how to prove theorems, the author assumes you already know how to do that. Consequently, I didn't master that skill. It also would have helped if the Solutions Manual that accompanies this text were available to students; maybe by now they've made it available. Leon definitely does not include enough worked examples in the text, and those problems where "The Proof is left as an exercise for the reader" are useless and defeating. I wholeheartedly disagree with the review above that "if you can't handle this text, don't major in math, you don't have what it takes". Nonsense. Provided you give it your all, you can major in math, and understand Leon's text, even if you aren't blessed with sheer, infallible intellect.
Rating: 
Summary: good introduction
Review: A very good introduction to linear algebra. Explanations are very clear. A very good exposition on vector spaces. Overall a good buy for starting in this most interesting subject.
Rating:
Summary: Proofs: Simple, but not rigorous
Review: Background: Electrical engineering grad student. Lots of math. Prior linear algebra course.Reason to read book: Wanted a text to review proofs of many of the important theorems that are used in the matrix formulation of quantum mechanics. Stuff like why Hermitian matrices provide orthogonal eigenvectors and real eigenvalues. Also, wanted a review of vector spaces, basis sets, etc. That means pretty much most of the book. How much of the book I've studied: Most of the proofs in the entire book. Some of the worked problems. None of the exercises. Analysis: The book provides a comprehensive list of the useful proofs. However, the proofs are simple but not rigorous. They give you good insight on why the theorems are what they are, but they don't remove all doubt as to their validity.
Rating:
Summary: A Good Book on Linear Algebra
Review: First of all, I would like to say this book is not for beginers. If you have no idea what a matrix is, don't use this book. However if you have taken an introductory course in linear algebra or you already have a reasonably well foundation in this subject, then you should have no problem in understanding following the text. Although the explaination in this book is not particularly outstanding, it does treat some advanced topics like eigenvalues, numerical linear algebra elegantly. I would like to recommend this book to persons who would like to seek a more advanced linear algebra book for reference or self studying. Finally, regarding to other reviews on this book, I would like to point out: 1. Linear algebra courses usually won't teach you how to prove. Go and take analysis courses if you like proving theorems. 2. If you are an absolute beginner, take some introductory courses on linear algebra FIRST before you take courses that use this book. I don't think any college will use this book in the first course in linear algebra.
Rating:
Summary: A Good Book on Linear Algebra
Review: First of all, I would like to say this book is not for beginers. If you have no idea what a matrix is, don't use this book. However if you have taken an introductory course in linear algebra or you already have a reasonably well foundation in this subject, then you should have no problem in understanding following the text. Although the explaination in this book is not particularly outstanding, it does treat some advanced topics like eigenvalues, numerical linear algebra elegantly. I would like to recommend this book to persons who would like to seek a more advanced linear algebra book for reference or self studying. Finally, regarding to other reviews on this book, I would like to point out: 1. Linear algebra courses usually won't teach you how to prove. Go and take analysis courses if you like proving theorems. 2. If you are an absolute beginner, take some introductory courses on linear algebra FIRST before you take courses that use this book. I don't think any college will use this book in the first course in linear algebra.
Rating: 
Summary: Great for "fixing holes"!
Review: I found this book great in order to "fix holes' in my mathematical weaponry or to get a quick review of things I needed; but I think that the way in which the theoretical stuff is developed is sometimes not very clear to those folks who have to tackle with the subject for the very first time. The applications are a remarkable feature of this book, introducing the reader to some very interesting applications of linear algebra in a variety of fields.
Rating:
Summary: Starts Off Great, Wears Down
Review: I used this Linear Algebra text in an undergraduate Linear Algebra course. Before I get to the problems of the text (and there are numerous) let me just say that it is conceptually complete, in that every topic in linear algebra is given very close attention. (Eigenvectors/Eignenvalues were given a very elegant treatment, as an example) All the concepts are well organized and also some applications are thrown in to the mix. With the above statement, it seems that this book has everything going for it to be a fantastic linear algebra book. Unfortunately, it hits some pitfalls. Although its conceptually complete, it is very dense. ( a common math textbook pitfall) Places where explanations could have been expanded quite a bit are not. Being a very dense math textbook leads to the next problem. Leon's notation is unneccasarily formal for an introductory linear algebra text. It is quite fustrating getting used to notation before you get to the key concepts. (His notation is not often explained well enough.) Although I got passed the overlyformal notation and got to the meaty concepts, I can completely sympathize with others who get stuck on it and have absolutely *NO* clue what the author is trying to say. Let's face it, not everyone taking Linear Algebra is a math major (I for one am a physics major and there were quite a few engineering majors in my class.) Another pitfall of this book is the absolute decrepid writing style. Do not laugh when [someone] states that this book is boring and well "Just not fun..." because that statement is the truth! The writing style has a very sleep-inducing tone, which is a shame because linear algebra is a very important topic and an interesting one. (With far reaching applications.) It is very difficult to describe... get through the book without much trouble and you will see what we mean. The only concrete example I could think of is the mind-numbingly dry explanation of vector spaces in the third chapter. In closing, this book does not need much to become a great linear algebra book. All the concepts are there, so the hard part is done. Hopefully Leon in the 6th edition will clean up the notation a bit and add some life into the explanations and writing style, this book could be an undergraduate linear algebra standard.
Rating:
Summary: Flawed, but conceptually complete.
Review: I used this Linear Algebra text in an undergraduate Linear Algebra course. Before I get to the problems of the text (and there are numerous) let me just say that it is conceptually complete, in that every topic in linear algebra is given very close attention. (Eigenvectors/Eignenvalues were given a very elegant treatment, as an example) All the concepts are well organized and also some applications are thrown in to the mix. With the above statement, it seems that this book has everything going for it to be a fantastic linear algebra book. Unfortunately, it hits some pitfalls. Although its conceptually complete, it is very dense. ( a common math textbook pitfall) Places where explanations could have been expanded quite a bit are not. Being a very dense math textbook leads to the next problem. Leon's notation is unneccasarily formal for an introductory linear algebra text. It is quite fustrating getting used to notation before you get to the key concepts. (His notation is not often explained well enough.) Although I got passed the overlyformal notation and got to the meaty concepts, I can completely sympathize with others who get stuck on it and have absolutely *NO* clue what the author is trying to say. Let's face it, not everyone taking Linear Algebra is a math major (I for one am a physics major and there were quite a few engineering majors in my class.) Another pitfall of this book is the absolute decrepid writing style. Do not laugh when [someone] states that this book is boring and well "Just not fun..." because that statement is the truth! The writing style has a very sleep-inducing tone, which is a shame because linear algebra is a very important topic and an interesting one. (With far reaching applications.) It is very difficult to describe... get through the book without much trouble and you will see what we mean. The only concrete example I could think of is the mind-numbingly dry explanation of vector spaces in the third chapter. In closing, this book does not need much to become a great linear algebra book. All the concepts are there, so the hard part is done. Hopefully Leon in the 6th edition will clean up the notation a bit and add some life into the explanations and writing style, this book could be an undergraduate linear algebra standard.
Rating: 
Summary: don't waste your money
Review: If you buy this book then get used to phrases such as: "It can easly be seen that...." and "It can be shown that..." and let us not forget everyone's favorite "...which is left as an exercise for the reader." You will see at least one of these phrases in every section (yes section not chapter). ... For [the money] I think Leon could work out just 1 example in detail. Fortunately there is enough information on the internet you won't need to read this book, instead just carry it around so your professor thinks your using it (although it makes a great door stop when you done with the class). Overall I think that 1 star is too much for this but Amazon won't let me give it 0 stars.
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