Customer Reviews

Linear Algebra With Applications

5 star:		(1)
4 star:		(2)
3 star:		(4)
2 star:		(2)
1 star:		(1)

 

 

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.

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.

The preface clearly states that this book can be used by beginning students "with little trouble reading and understanding the material". This is both patent nonsense and a clear indication that the author long ago forgot that the beginning student is indeed just a beginner. From this particular beginner's viewpoint, the one star rating is one star too many. I'm a junior majoring in math and computer science with above average grades and only mention it as a prelude to my opinion that, at the sophomore undergraduate level, which this text purports to accomodate, the material, as presented, borders on incomprehensible. Time after time I read, re-read and re-re-read sections of text and was unable to glean the slightest bit of information from the extremely advanced presentations by the author. Explanations are often incomplete from the "beginner's" viewpoint and are made with the use of a very complex notation. After these laborious exercises, and with the help of my instructor's lectures, I would finally come to understand the material and wonder why it needed to be presented in such a ridiculously complicated manner. The very last straw was when I reviewed the text for exams and found errors. Mr. Leon seems to have the ability to take a difficult yet manageable subject and make it read like a foreign language. I discussed this with several members of my class who also admitted to being totally befuddled by way the material was presented. Even my instructor at one point claimed to have a difficult time with certain sections and had to write a different version so that it could be understood. I'm sure that this book must have some redeeming value for more advanced mathematical study, but it is definitely not what it is represented to be; a text to accomodate a beginners' class in Linear Algebra. I'm happy to say I did well in the course, but it was in spite of this textbook and certainly not because of it. Also, not nearly as important, but perhaps pertinent to those thinking of investing $69, the book literally fell apart after 4 months of reasonably careful use. It is poorly constructed of cheap materials and even the ink smears when you touch it. What a disappointment!

many steps and explanations are left out because they are assumed to be 'obvious'. i did not find them to be that easy to figure out.

Leon makes a commendable effort to make this book readable with color figures and applied examples of his topics. Unfortunately his familiarity with the topic has caused him to make the common mistake of leaving out mathematical steps and explanations under the assumption that they are trivial and obvious. Additionally he often brings up a topic or theorem and leaves the proof as an exercise for the reader. Exercises for the reader are not supposed to be discussions in the text, they are called Exercises and are listed in the back of the section as homework.

In summary it was a good effort, but he falls in the common trap of mathematical books that has the author write at their own level of comprehension.

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.

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.

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.

this provides a rather solid background for those in higher mathematics. id say it is suited for the advanced student due to the simplistic nature of explanations.

Let me start off by saying that I do not mean to offend the other reviewers with what I have to say. Also, admittedly, I have not read this text fully. But I am in a position to write this review since I turored students using this text.

First, this text is not very difficult. The problems are very straight forward (including the simple proof exercises). The material is presented in a very "beginnerish" fasion. But since linear algebra is the class which provides a bridge to higher mathematics, the exposition must be mathematical to some degree. If this text disagrees with you for the reason that this book is too hard, you should not be majoring in mathematics, you do not have what it takes (or equally likely, you have not put enough effort into the class, i.e. studying the text)!

My reasons for disliking the text are rather different, I very much dislike this text since it is so dull. The text, in some odd way, is very boring, as opposed to texts such as Strang or better yet Hoffman/Kunze (this is my preffered text for highly motivated students). I wish that I could eloborate more in words but I can not. For those of you who have read the text and do not find it too difficult, I am quite sure that you know what I am talking about.

I am giving this text 2 stars because "it is just not fun," as vague as that sounds. It is not a good book for refrence, self-study, or as a class text. I feel guilty giving 2 stars without being able to explain just why, but I am going with my feelings on this one. note: sorry for any spelling errors, I am in a rush and do not have time to check. Please forgive my haste.