Customer Reviews

Linear Algebra: A Geometric Approach

5 star:		(2)
4 star:		(3)
3 star:		(0)
2 star:		(1)
1 star:		(7)

 

 

Again I was puzzled that such a fine book by such fine authors could receive several pans here. Looking at it again I see why. As usual it is because the book gives the reader more than some of them want, and hence expects more from them in turn.

Instead of merely exhibiting pages of sterile computations with rows of matrices and linear equations, but no visible meaning, the authors begin with a short and useful review of the geometry of vectors in the plane, including ways of computing angles via dot products. Using the ideas developed there, they expand to discuss n dimensional vector geometry, and pose the problem of describing hyperplanes in n space, i.e. copies of n-1 dimensional subspaces embedded linearly in n space. Of course these ideas are already challenging.

Why do they do this? Because this is exactly what the solutions of a linear equation in n variables represents. One equation represents one hyperplane. Hence several simultaneous equations represent the intersection of several hyperplanes. that's all folks.

The accompanying geometry reveals exactly why 2 equations in 3 variables are expected to have infinitely many solutions: it is because the two planes represented by the two equations, intersect generally along a line in 3 space. But the uncurious student who does not care what solutions of equations mean, is annoyed rather than enlightened.

This is unfortunate, but the authors are rather to be complemented for explaining not only how calculations in the subject are carried out, but what they mean geometrically, and also how they can be applied in many situations. Perhaps the deepest applications, to differential operators, occurs as well at the end of the book.

All in all a fine book for some one who wants to understand not just the numerology, but also the geometry of linear algebra, i.e. the interpretation that gives intuitive substance to all the theorems.

When looking over the reviews of a college textbook, one must take care not to fall into the fallacy of accepting a study where the selection is extremely non-random. Students who take a course where a specific book is used and have difficulty with the material tend to be the ones who try to get even by writing horrific reviews. This book is nowhere near as bad as the comments of other reviewers would lead you to believe.
I teach mathematics at the college level and examined this book for possible adoption as the text for a course in linear algebra. While my teaching assignment was changed so I was no longer teaching the course, there is no question that this book would have been suitable.
There are many worked examples and they are clear, thorough and yet concise. A diagram is included when necessary but there are no cases where a diagram is superfluous. The coverage is that of a traditional linear algebra course and there are special sections on:

*) Complex eigenvalues and Jordan canonical form
*) Computer graphics and geometry
*) Matrix exponentials and differential equations

Solutions to the majority of the exercises are included in an appendix.
Linear algebra is the traditional transition course in the math major, where the student bridges from what is sometimes called the "plug and chug" level of mathematics to the "theorem-proof" level. In this book, the authors take an appropriate approach to this transition, using geometry as much as possible to aid in the understanding of what the constructs of linear algebra are.

Let me first say that I attend Duke, enjoy math, get good grades in math, and am willing to put in the hours to understand something. But I think that it is very telling that those who teach linear algebra and those who learn linear algebra have very different attitudes towards this book.

The parts where the book explains something with diagrams, explains a proof, or puts forth a definition are generally quite good. The concepts are exacty what I want to learn. I would ask that the book be a little more directed towards beginners and not assume that repitition of concepts is unnecessary, but I have no major complaints about that part.

The huge, glaring, fatal weakness of this book is that there are nowhere near enough examples and practice problems. I took notes on each section, worked through each example multiple times, and make a sincere effort to do every single one of the exercises (don't tell me I haven't put in enough effort, because I've been nearly ignorning my other classes to spend hours every day trying to puzzle out this book).

I consider myself a math and science person, and I am doing everything I can. But the simple fact is that I need more examples. More explanations of problems. More ways to practice what I'm trying to learn.

I'm fine with a challenging text, but there's a difference between challenging and simply frustrating. I don't want the text to become any easier, I just want a way to improve my understanding of it, and I don't think the current amount of exercises and examples are anywhere near adequate.

To be perfectly clear, DO NOT purchase this book for self-study unless you already are quite familiar with linear algebra. If you know and love linear algebra pretty well already, I can see how this book might be useful.

This was my favorite textbook in college and the only one I ever came close to reading straight through. I had it for a Linear Algebra class as a sophomore at Duke back in the fall of 2004. I enjoyed the conversational style, the connections between algebra and geometry, and the amusing footnotes. I do remember finding the material to be challenging, and at least one time I had to ask the professor for clarification of something in the text that I found to be confusing, but overall I thought it was very good, and it worked out well for me: I went to class, read the book, did the homework problems, and got an A.

If you are a beginner in linear algebra, and probably at your first year in engineering/physics/computer science, then I don't recommend this book. I'we been stumbling throught it the past few months, and was doomed to fail my test...

but about a week before the test I got another book called Linear Algebra, a modern introduction, by David Poole. I can surely say that this book saved me. The examples and descriptions are very good, and the author has a sense of knowing what parts might get you confused, and what you might want to review from earlier chapters. It seems that every time I got confused, then the next sentence was exactly the answer to my question.

Now regarding the Theodore book, a really bad downside is that there is no solutions manual available, and there are only answers to about 5-10% of the exercises! This book is also very unorganized, and rather hard to find something you look for. It's written in a "continuous" way... meaning that there aren't clear enough marks of when something ends and another thing starts. And there isn't even a clear point in the things the authors are explaining. Sometimes just examples, with no beginning problem, and no real results.

So bottom line, if your a beginner, get the David Poole book!

If your not a beginner though (or really excellent in math), then this book (the Theodore one) isn't so bad, it comes up with some nice examples and really makes you struggle in the examples and exercises.

Simply stated, this is the worst textbook I have ever used or seen in my life. Poorly organized and terribly written, this text may be fine for someone who has already had linear algebra and wants a compact review of the material, but it is an absolutely terrible source to learn from. The author does an incredibly poor job of explaining the concepts and mathematics behind linear algebra, forcing the student to learn the material completely on his own using other sources. My professor remarked one day that this is the best book on the market. If so, the market is in a very sad state right now. Do yourself a favor and get another book, and if you're a professor, for the love of your students and mathematics, DO NOT USE THIS BOOK IN THE CLASSROOM.

I gave this book one star only becasue there was no 0 star rating, this is the worst math book I have ever used. It is poorly written, there are lots of mistakes( which to this date 05/29/03, that have not been correted on the authors' web page). This book was poorly organized, over priced, and had a weak book binding (my copy began to fall apart!!).
Please do not buy this book, unless you like to waste your money on useless material.

For the amount of money i paid for this book it should be a lot better than it is. It's very poor that a book that costs over $100 should have weak binding and fall apart after less than 6 weeks!!! It's not just me..friends of mine also have copies that are falling apart. Poorly written and strange at best... Caveat Emptor!

It has been said a few times already but I'll just reiterate. This book is horrible. I went into this class having been told that Linear Algebra is a reasonable subject. Not so with Shifrin and Adams. The lessons do a very poor job of prepping you for the included exercises. Unless you have an exceptional professor be weary of this one.

This book is horrible. Not only does it do an awful job of teaching you linear algebra, but the book itself falls apart pretty easily. Now I'm stuck with this (way to expensive) book and I won't be able to sell it since people tend to like the pages to be in the book when they buy it. For the record, I do like linear algebra, but that interest was developed by my professor but not by this book in any way.