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on December 10, 2015
I completed this book as an undergraduate introductory course to linear algebra and formal proofs. The lucid explanations make the book ideal for someone without a lot of mathematical background. It was a joy to read, and the exercises are usually accessible and assume no prior knowledge — only a small fraction of problems are very involved.

But the material is mostly theoretically interesting, and does not cover many of the computational tricks in a normal linear algebra class — Gauss-Jordan elimination, a hugely important topic, is not even mentioned. There are so many other things missing, like calculations. You work more with operators and vector spaces than with matrices, and finishing this book won't help you understand the matrix terminology that's common in linear algebra. The book is more suited as a primer to a higher-level theoretical class, like operator theory, functional analysis, or modern algebra. It cannot be a prerequisite to practical/applied courses, like, say, statistics or machine learning. I feel like I've learned a lot after finishing the book, but I don't feel prepared for courses that require a 'working knowledge' of linear algebra.

If you're at all interested in theoretical aspects of algebra or being gently introduced to good proofs, this book will appeal to you. I had never done theoretical math before, and this book was interesting and accessible.
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on April 24, 2011
Although the text on the cover says that this is intended as a second course in linear algebra, I think that it is totally suitable as a first one for a pure math student.
The book conveys the issential idea of linearity in mathematics without delving into arithmetical calculations with matrices, which usually appear in standart linear algebra texts. Most of the theorems which are considered quite advanced in standart texts are shockingly simple due to the more abstract approach.
The only objection to this approach I can imagine is that the text doesn't teach you much of matrix arithmetic. But in my opinion, the necessary amount of computational techniques one will learn anyway. The course I learned had the opposite problem - alsmost the whole semester we spent on Ax=b problem and its variations, so we learned an overwhelming amount of arithmetic with almost no theory, which wasn't very useful.
This is THE book for a pure math major learning linear algebra
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on July 2, 2014
I stumbled on this book when I realized my preparation in Linear Algebra was relatively weak. I'm a software engineer and wanted to refresh my understanding of basic math. In University, I took a linear algebra using Lay's book which focused primarily on matrices and the computational aspects of eigenvalues, determinants, and applications. I read this book and completed the majority of exercises and came out with a solid conceptual understanding of linear maps, eigenvalues and eigenvectors, inner product spaces, and canonical forms. This book is excellent for self study even if you aren't a math major.
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on October 1, 2017
I have used this book in class several times, and I find it to be very good. The third edition adds material on dual spaces and quotient spaces, which is good for undergraduates who can deal with more mathematical abstraction.
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on September 30, 2014
My husband used this to supplement his senior level, undergraduate linear algebra course. His professor had required another text, but my husband found he got more information out of this book than from the required text. At the end of the semester, turned out, the professor was carrying around this text and had been teaching out of it as well. Seemed to have helped him get his A.
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on July 11, 2016
The writing is clear and easy to understand. It's really a pleasure to read. If you've had a taste of linear algebra and would like to study it on your own, this is one of the best books at the appropriate level.
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VINE VOICEon March 8, 2009
This was the textbook for a course entitled Advanced Linear Algebra that I took as an undergraduate. I remember it fondly. The author believes that students of linear algebra learn to think too narrowly by being taught to use matrices for everything; thus, matrices are not introduced until late in the book. The approach is novel, and the book succeeds in showing the larger world of linear algebra beyond matrix operations. However, this does make the book mainly suitable for mathematicians (and perhaps physicists); for those who want to learn typical applications of linear algebra, look elsewhere.
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on June 2, 2004
This is a short, elegant presentation of linear algebra appropriate for upper level undergraduate math majors with a theoretical bent. The student has perhaps taken a linear algebra course designed for engineers and scientists. Such a student is comfortable reading mathematics and writing proofs. It is meant to be read and re-read until the ideas are absorbed. The exercises are relatively easy and no answers are provided. With exercises of this sort you generally know if you are on the right track and they require you to understand the presentation in the text and process the ideas in a straight forward way.
Of course, there is nothing in this book about applications or the computational aspects of applying linear algebra.
The price is right. This could be a very useful purchase even if it's not assigned as a text.
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on September 25, 2017
The book is in perfect shape and is exactly what I needed for my class.
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on November 29, 2008
I have found this book to be quite readable, but it is very abstract. I am not sure if persons who are looking for the applications of Linear Algebra would appreciate this book very much. This book requires mathematical maturity. Some of the problems at the end of the chapters are straight forward where as others are very challenging. This book is sort of rigorous, but there are others out there that are even more rigorous. Overall, I think this book is very good for those with a good mathematical foundation, but I don't think it's the best.
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