Not for beginners in linear algebra
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.
Very suitable for use as a text in a linear algebra course
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.
Horrible Book
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.
Awful book
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.
a fine book telling you what the numbers mean
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.
(11 reviews)
