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Linear and Geometric Algebra
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Top Customer Reviews
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.Read more ›
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.
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.Read more ›
Most Recent Customer Reviews
I would certainly agree with all of the other "5 star" reviewers. I've read this book and worked nearly every problem - the book is well written, in my opinion deserving... Read morePublished 14 months ago by Michael Hardin
I'm no expert on linear algebra, rather just an older student who sees a lot of connections to various interesting corners of mathematics. Read morePublished 17 months ago by reeder
A great review of linear algebra and a great introduction to geometric algebra. I am still working on fully understanding how to apply GA, but the additional insights about linear... Read morePublished 17 months ago by Leonard Mygatt
I really struggle with Linear Algebra, but this book cleared up a lot of things for me. I really like his writing style and that everything is covered in very good detail.Published 18 months ago by Tash
This book is not very well suited for self-study. The material presented (Geometric Algebra) is at times difficult to understand and as there are no solutions to the problems you... Read morePublished on August 3, 2014 by A.A.J. Geeraert
Great presentation. Great transition from linear algebra to geometric algebra. I wish universities would have this course available as an undergrad course.Published on April 15, 2014 by Life long learner
Macdonald introduces the geometric algebra in a clear and logical manner. The link between the geometric algebra framework, with its focus on coordinate-free (= basis independent)... Read morePublished on November 7, 2013 by K.H.I. Reenders
This is really a good book: succinct and yet informative. With plenty of exercises, of course. I had some idea that this geometric geometry is related to linear geometry, but not a... Read morePublished on August 25, 2013 by Nick