Customer Reviews: Read 39 more reviews...
 good first introduction August 19, 2008
This book is good for a basic introduction, that is for people who have never really seen much linear algebra and who haven't taken a proof-based course before. I used it in my first linear algebra course as an undergrad, and also when I taught an introductory course over the summer.
I especially like that it has some options, such as details of R^n being presented at the end of chapter two as an alternative to covering those facts in the more general context of "vector spaces" in chapter 4. It is not especially rigorous as far as proving things, and does not get too in depth as far as computations though there are some good sections on dynamical systems. So if you are teaching a class that is half engineers and half math majors, it strikes a decent balance.
For anyone who uses linear algebra, you will not be able to get away with having this as your only book, try Strang or Axler for more computational or theoretical (respectively) treatments. It is definitely a good intro though, it gives a decent overview of the main ideas.
 Incredibly Accessible August 17, 2007
1 out of 1 found this review helpful
I used this book to teach myself linear algebra using a lesson plan developed by a teacher. A few things I found really helpful:
Lay constantly admonishes the reader to carefully study the text, by reading and re-reading. He understands that students learning linear algebra are likely to to be embarking on more abstract/advanced mathematics in the future--and he cares enough to teach good study skills as well as math. I've followed his advice, and found that with proper effort, I am able to teach myself.
Many of the questions are conceptual or True/False, which helps me to retain new concepts.
The study guide (sold separately, but very important if you're self-teaching) only includes answers to odd-numbered exercises. However, the answers are nicely detailed.
I especially appreciate that Lay refuses to flat-out offer answers to conceptual and True/False questions. Instead, there are hints and references to page numbers where helpful information can be found. This is important, not only because it (again) helps reinforce good study skills, but it encourages students to really try a problem before giving up and looking up the answer.
The introduction of new concepts is always followed by one or more examples, which helps to link theory to practice. In general, there are many examples that illustrate good problem-solving techniques. Proofs are detailed and well-justified, and there are some simple proofs that are left as problems in the book. These proofs are simple enough to not be terribly daunting to the student who is new to more abstract mathematical ideas.
For the student who would ask, "well what is it good for?" there are plenty of sections dedicated purely to applications of material learned in previous sections.
Detail-oriented methodical learners like myself should benefit from this book.
 a good teacher helps... July 31, 2007
0 out of 1 found this review helpful
covers 75% of the detail and leaves the 25% up to you. it lacks clear explition is vector space secotion (row col vector nul basis etc). it seems like you do the first coumple of sections not understanding what you are getting at but when you get to chapter 6 or so the past stuff finaly makes sense. I found the book hard to understand when it was talking about maping, one to one on too. i suggest a TI-83 or higher and the solutions manual. The book also lacks pictures showing dimention row col nul basis etc.
 Choose Another Book July 30, 2007
The organization and the treatment given to most subjects are well below what one would expect for a Wikipedia entry on each respective topic.
Anyone who uses this book for any kind of self-study is unlikely to get more out of it more than a few examples on multiplying matrices, row reduction, and some poetry about eigen-spaces and vector spaces.
Take a look at ``Linear Algebra Done Right'' by Alxr.
meh..... May 14, 2007
2 out of 2 found this review helpful
This was the textbook that my school has been using for its first and second year Linear Algebra courses. I found it somewhat terse. It seems like it could be a great book for someone already familiar with linear algebra or the logic aspect of mathematics; I don't recommend it for anyone who is not very familiar with proofs. Fortunately, it doesn't lack examples of how to solve computation problems and solutions to the odd-numbered problems are provided in the back of the book. Unfortunately, when it comes to the proof problems, instead of just providing the reader with the answer like most other texts, the author will either mention a hint or refer the reader to the study guide (mine came with a disk which has to be installed on a computer), which could be a problem for readers not familiar with how to do proofs. Serving as a somewhat of a mediator between these two extremes are true/false questions which accompany each chapter in each section of the text. While those start out somewhat fun in the beginning, they can also get tiresome and repetive very quickly. The solutions to these, like the proofs, are not provided, but fortunately, all one has to do is read the text carefully in order to determine the appropriate response.
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