A Vector Space Approach to Geometry (Dover Books on Mathematics) Paperback – 28 Mar 2003
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Most Helpful Customer Reviews on Amazon.com (beta)
The almost four hundred pages book is remarkably readable and is very consistent at that. There are both worked out examples and exercise problems, for each section - which are very useful for self-study or revision.
If you have never had an introduction to linear algebra before, you may have to supplement this with a linear algebra book. But if you have not had a good course in elementary geometry, and your motivation is getting started with elementary Computer Graphics/CAD and the likes, this is a good book for that.
Interspersed with the subject matter discussed at a elementary level, in a useful, stimulating style are small, interesting discussions on such useful and relatively advanced topics as function spaces, fixed point theorem in affine transformation, simplices, symmetries etc. I rarely have seen any of these topics mentioned in a book aimed at this level.
Highly recommended for freshman undergraduates and those without any mathematics experience who want to start in Graphics, CAD, CAGD and the likes. Recommended also for experienced practitioners in Graphics: it is good to review the fundamentals once in a while, and a well written book that is a quick read helps at that!
It is a formal math book, with axioms, but it is strong on motivation and has some quite amusing examples.
Keywords: tangent spaces, determinants, barycentric, linear transformations.
It also is full of other interesting insights and relations to other topics, including some applications to Calculus (motion) and some topology.
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