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Practical Linear Algebra: A Geometry Toolbox

4.1 out of 5 stars 9 customer reviews
ISBN-13: 978-1568812342
ISBN-10: 1568812345
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Editorial Reviews

Review

" Read an article on teaching Linear Algebra written by Gerald Farin and Dianne Hansford. -Ties Magazine, November 2005
""It is well written and the examples are carefully chosen to motivate or exemplify the topic at hand."" -J.R. Burke, CHOICE Magazine , September 2005
""[The] mixture of linear algebra, geometry, and numerical aspects is very interesting and will probably stimulate the students."" -Yves Felix, Bulletin of the Belgian Mathematical Society, December 2005
""I picked up this book with the thought, 'oh, another linear algebra text.' I was pleasantly surprised, upon examination, that it is not just another one. The standard linear algebra material is presented with good motivating stories, illustrations and examples."" -S. Swaminathan, CMS Notes, February 2006
""This book covers all the fundamental topics of linear algebra ... It is also an inspiring book for pure mathematicians who would like to learn more about applications of linear algebra ... a useful source of many nice examples."" -EMS, December 2006
""Das Buch [ist] eine einmalige und wertvolle Ergänzung zur bestehenden reichen Literatur zur Linearen Algebra."" -Internationale Mathematische Nachrichten, April 2007"

About the Author

Gerald Farin received his Pd.D. in Mathematics from the University of Braunschweig, Germany, in 1979. He is the author of the texts "Curves and Surfaces for CAGD" (5th ed.), "NURBS" (2nd ed.), "The Geometry Toolbox", and "Essentials for CAGD". He is the editor-in-chief of "Computer Aided Geometric Design". Dianne Hansford received her Ph.D. in Computer Science from Arizona State University in 1991. Since 1995 she has been a faculty associate at ASU's computer science department, occasionally teaching Computer Aided Geometric Design (CAGD) and Computer Graphics. She has published several research papers in the field of CAGD and is coauthor of the books "The Geometry Toolbox" and "Essentials for CAGD".
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Product Details

  • Hardcover: 400 pages
  • Publisher: A K Peters/CRC Press (December 21, 2004)
  • Language: English
  • ISBN-10: 1568812345
  • ISBN-13: 978-1568812342
  • Product Dimensions: 9.8 x 7.6 x 1 inches
  • Shipping Weight: 1.9 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #1,465,409 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Joshua Davies VINE VOICE on July 21, 2008
Format: Hardcover Verified Purchase
I have to say this book was perfect. It's written with the assumption that you know algebra and trigonometry (you'll also need a little bit of calculus if you want to completely absorb chapter 18) and goes from there to describe linear algebra step-by-step. I was struggling with concepts like Eigenvectors, Gaussian elimination, matrix inversion, etc. but after reading through this book and working all the exercises (most of which have answers in the back for self-study), I'm actually finding myself "thinking" in linear algebra.

The first third or so of the book covers 2D linear algebra, and has a bit of a bias towards graphics problems. It covers things like line intersections and "closest point to a line" as well as rotations, shears, translations, etc. The next third or so extends these concepts out to 3D (still with sort of a graphics bias) and introduces 3D-only concepts such as the cross product. Finally, the last third introduces the abstract N-dimensional perspective that doesn't have a graphical interpretation. This is where it discusses things like least-squares estimation and orthonormalization - the really useful (but abstract) bits of linear algebra.

With the first two thirds of the book to back it up, I found the really abstract concepts (which most authors seem to want to start with) relatively easy to absorb - which is really a pretty amazing accomplishment.

I also can't recommend the chapter exercises highly enough. Most of them had answers in the back, so you can check your work (including these ought to be a no-brainer for writers of math books, but evidently there are quite a few math book writers with, well, no brains...
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Format: Hardcover
This is a very good book for learning Linear Algebra. It succeeds is two important ways. One it helps you build an intuitive understanding of the subject, something more theoretical books sometimes fail to do. Second, it helps you build a nice toolkit for working with 2D and 3D geometric models.

So, it covers the normal topics of Linear Algebra, vectors, matrices, determinants, Gaussian elimination, eigenvalues, etc. But, it also mixes in topics from Computer Graphics such as points, lines, planes, polygons and Bezier curves. By doing so, it demonstrates just how useful Linear Algebra is for geometric transformations such as scaling, rotation, and translation.

Math majors will want to go beyond this book. There are several books that give a more comprehensive treatment of this subject. But, even to those readers, I suggest you try this one first.
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Format: Hardcover
I LOVE THIS BOOK!
The Linear Algebra course at my college uses Otto Bretscher's book, and not this Geometry Toolbox book, but this Geometry Toolbox is just so awesome!
It's a must have. Basically it gets rid of all the definition, proof, theorem nonsense and gives you fun pictures! You get to think of linear algebra in terms of 'this matrix make the picture move sideways' instead of 'theorem proof Ax=[xxuiahsifuha][asdg][ah][hhh] what????'
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Format: Hardcover Verified Purchase
This book takes a visual approach to linear algebra. Assertions are demonstrated pictorially in elegant ways that make the subject obvious. This is THE linear algebra resource for novice students, with the exception of those who love the obscure proof and axiom driven explication common of other linear algebra texts.

Authors - next time go further. Although featured in the index, explanation of deeper topics like singular value decomposition and least squares regression is lacking. In the next edition expand it to the next level.

As an engineer, if I ever teach this subject this is the class textbook.
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Format: Hardcover
This is a very practical and useful book on linear algebra for students and practitioners in computer graphics and computer science in general. Its practical approach based on its strong visual geometric component will also appeal to students who find other linear algebra books to be a wee bit too dry and theoretical for their tastes.
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