Linear Algebra: A Geometric Approach (Hardcover)

by Ted Shifrin (Author), Malcolm Adams (Author)

Editorial Reviews

Product Description

Introducing students to a subject that lies at the foundations of modern mathematics, physics, statistics, and many other disciplines, Linear Algebra: A Geometric Approach appeals to science and engineering students as well as mathematics students making the transition to more abstract advanced courses.  One of the goals of this text is to help students learn to think about mathematical concepts and to write rigorous mathematical arguments. The authors do not presuppose any exposure to vectors or vector algebra, and only a passing acquaintance with the derivative and integral is required for certain (optional) topics.

About the Author
TED SHIFRIN, University of Georgia. - MALCOLM ADAMS, University of Georgia.

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Product Details Hardcover: 464 pages Publisher: W. H. Freeman; illustrated edition edition (August 24, 2001) Language: English ISBN-10: 071674337X ISBN-13: 978-0716743378 Product Dimensions: 9.3 x 7.1 x 1.1 inches Shipping Weight: 1.9 pounds (View shipping rates and policies) Average Customer Review: 2.8 out of 5 stars See all reviews (14 customer reviews) Amazon.com Sales Rank: #684,008 in Books (See Bestsellers in Books)

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Customer Reviews

14 Reviews 5 star:  (4) 4 star:  (3) 3 star:    (0) 2 star:    (0) 1 star:  (7)           Average Customer Review 2.8 out of 5 stars (14 customer reviews)		Share your thoughts with other customers:
Most Helpful Customer Reviews 7 of 7 people found the following review helpful: 5.0 out of 5 stars Update, February 2, 2004 By  Ted Shifrin "shifrin" (Athens, GA) - See all my reviews The authors very much appreciate the feedback that has been posted here. Due in large part to the hue and cry from the students at Duke University (several of whom posted their outrage here) as well as from many of our own, Freeman has put out a new printing and we hope that the binding problems will have been solved. The most egregious typos of which we were aware have also been fixed. The authors are most anxious to hear from you directly if you find typos or have complaints about unreadable sections, misleading exercises, and so on. (Hey, we had to fill in the rating! We tried to leave it blank, but the computer wouldn't let us!) 12 of 14 people found the following review helpful: 4.0 out of 5 stars a fine book telling you what the numbers mean, September 20, 2004 By  twit - See all my reviews 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. 4 of 5 people found the following review helpful: 4.0 out of 5 stars Very suitable for use as a text in a linear algebra course, December 7, 2006 By  Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)       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.		Ad feedback   Most Recent Customer Reviews 5.0 out of 5 stars exceeded expectations book was in new condition as advertised and got to me in the least amount of time projected. very satisfied with purchase. Published 21 days ago by M. Barton 5.0 out of 5 stars Great! The product got here in the specified time and was exactly what I ordered. Saving $70 made me happy, as I'm sure it would anyone. Published 4 months ago by K. Burns 4.0 out of 5 stars Linear Algebra: A Geometric Approach A required textbook at a better price. I intend to keep the book for reference therefore there is no insentive to buy and sell at the local bookstore. Read more Published 6 months ago by College Greg 1.0 out of 5 stars 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. Read more Published on May 9, 2007 by Frímann Freyr Kjerúlf Björnsson 1.0 out of 5 stars 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. Read more Published on September 12, 2005 by B. Johnson 1.0 out of 5 stars 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. Read more Published on May 6, 2005 by A reader 1.0 out of 5 stars agreed! worse math book EVER written this is by far the worse math book I have ever read in my life! not only is it hard to learn from the book due to the errors and bad workings, but the examples done in the book... Read more Published on February 22, 2004 5.0 out of 5 stars In fact it's a quite good book. I used it to review linear algebra before entering graduate school. It works good for me, although I already knew how the math part works. Read more Published on November 27, 2003 by Tianzhi Yang 1.0 out of 5 stars An Absolutely Terrible Text 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... Read more Published on October 31, 2003 1.0 out of 5 stars Poor 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... Read more Published on September 30, 2003 Search Customer Reviews Only search this product's reviews

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Product Details

• Hardcover: 464 pages
• Publisher: W. H. Freeman; illustrated edition edition (August 24, 2001)
• Language: English
• ISBN-10: 071674337X
• ISBN-13: 978-0716743378
• Product Dimensions: 9.3 x 7.1 x 1.1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 2.8 out of 5 stars See all reviews (14 customer reviews)
• Amazon.com Sales Rank: #684,008 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

7 of 7 people found the following review helpful:

5.0 out of 5 stars Update, February 2, 2004

By	Ted Shifrin "shifrin" (Athens, GA) - See all my reviews

The authors very much appreciate the feedback that has been posted here. Due in large part to the hue and cry from the students at Duke University (several of whom posted their outrage here) as well as from many of our own, Freeman has put out a new printing and we hope that the binding problems will have been solved. The most egregious typos of which we were aware have also been fixed.

The authors are most anxious to hear from you directly if you find typos or have complaints about unreadable sections, misleading exercises, and so on.

(Hey, we had to fill in the rating! We tried to leave it blank, but the computer wouldn't let us!)

12 of 14 people found the following review helpful:

4.0 out of 5 stars a fine book telling you what the numbers mean, September 20, 2004

By	twit - See all my reviews

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.

4 of 5 people found the following review helpful:

4.0 out of 5 stars Very suitable for use as a text in a linear algebra course, December 7, 2006

By	Charles Ashbacher "([e-mail])" (Marion, Iowa United States([e-mail])) - See all my reviews (TOP 50 REVIEWER)

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.