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Linear and Geometric Algebra Paperback – January 19, 2011

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Editorial Reviews


The combined linear and geometric algebra becomes a necessary, powerful tool or language within physics, computer science, and engineering. Recommended. - Choice

About the Author

Alan Macdonald is Professor Emeritus of Mathematics at Luther College in Decorah Iowa. He received a PhD in mathematics from The University of Michigan in 1970. His research interests include geometric algebra and the foundations of physics. His web page is at

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Product Details

  • Paperback: 220 pages
  • Publisher: CreateSpace Independent Publishing Platform (January 19, 2011)
  • Language: English
  • ISBN-10: 1453854932
  • ISBN-13: 978-1453854938
  • Product Dimensions: 6.7 x 0.5 x 9.6 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #312,161 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

78 of 80 people found the following review helpful By Jeffrey Dunham on May 27, 2011
Format: Paperback Verified Purchase
Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers, given that geometric algebra is not a standard part of the undergraduate mathematics, physics, or engineering curriculum.

Like most everyone else, I first became aware of geometric algebra through David Hestenes: his American Journal of Physics articles, his books, and the many materials available at his web site, all of which I can recommend. I've also spent considerable time with the geometric algebra book by Doran and Lasenby, as well the book by Dorst, Fontijne, and Mann. The aforementioned books can help you understand why it might be worth your while to learn geometric algebra. Should you decide geometric algebra is worth your while, and furthermore, decide to develop some pencil-and-paper proficiency with it, I recommend Macdonald's book as a great way to get started. It won't help you discover new applications of geometric algebra, but it will give you the mathematical background and confidence you need to move on to the more difficult books and articles with applications to science/engineering.

Macdonald writes in a consistently friendly, but serious, voice that suggests he cares whether or not a reader understands the reasoning behind proofs and appreciates the significance of the results obtained from them.
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37 of 38 people found the following review helpful By Norm Cimon on December 2, 2011
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Alan Macdonald has prepared for this for a long time. His personal web site at Luther College in Iowa includes an extensive list of his papers. That work shows clearly that he has both the mathematical and physical chops for this task. His detailed survey of geometric algebra and geometric calculus, which can be found on that site, has been worked and reworked since he first developed it in 2002. It is quite thorough in that it covers not just the fundamentals of the algebra, but also incorporates quite a few physical applications for motivation. For example, at this point it's well understood that quantum spin is really a geometric property of the particles themselves. Macdonald's survey covers that clearly and concisely.

Here he develops the first undergraduate text to cover the essentials of linear algebra, and its extension to geometric algebra. The terse statements from the above survey are expanded, in this elegant book, into rigorous proofs. Given the care with which that's done, however, it easily rewards those students for whom this is a first introduction to the abstract concepts inherent in linear vector spaces - and the higher dimensional analogues where the multi-vectors of geometrical algebra live.

I believe, as Macdonald does, that the geometric interpretation of Clifford algebras, and its extension to geometric calculus "unify, simplify, and generalize vast areas of mathematics". I'd strongly recommend this book to engineering, computer science, and physics teachers. It provides a solid grounding in this important and emerging area of mathematics.
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24 of 24 people found the following review helpful By David Eaton on December 21, 2012
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I had never heard of geometrical algebra until I stumbled across it in some books about physics. If I had to pick out something that I have learned since school that I found enlightening, what I know about geometric algebra would be it.

Macdonald wrote this as a book for a linear algebra course; most of us in science or engineering encountered lots of linear algebra, and so I can't review this book as a first intro to linear algebra.

But, assuming you have seen some linear algebra, it isn't a bad description to say that geometric algebra is an extension to other things (like planes and 3D figures) in a particularly appealing manner. There are a few routes into thinking about, for instance, rotations in 3D. I always thought of them as typical coordinate transformations, something I might need in a physics problem or to do some graphics programming.

But it turns out that there is far more going on, and the language of geometric algebra is a very good means of expressing this sort of thing. And because Macdonald builds it up on something pretty familiar to those with some college math, it is accessible in a way that a lot of the more advanced or scholarly works available don't provide as well. It is a fairly short book, and it is well-written and accessible.

If you are rusty with linear algebra, it might be nice to have a more traditional text around, because the author does not do a lot of the mechanical things one usually does in a course on matrix or linear algebra; he (correctly, I think) de-emphasizes the workaday calculation of things like determinants or inverting matrices to have more time and space for more geometric algebra, which is as nice as a language for reasoning as it is a calculation tool.
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