Paving the way for geometric calculus, which replaces traditional vector calculus theorems (like Stokes' or Green's theorem) with one fundamental theorem. Finding the Book and Supplementary Materials
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Buy the Kindle edition, download the Kindle reader for your laptop/phone, and start with Chapter 1. Within a week, you will understand why David Hestenes called geometric algebra “the missing link” in mathematical education. And you will have Macdonald to thank for making it accessible to all.
Geometric algebra introduces the , denoted simply as ABcap A cap B for two vectors
The central argument of the text is that geometric algebra provides a that generalizes complex numbers, quaternions, and tensors into one system. alan macdonald linear and geometric algebra pdf
Macdonald doesn't just add GA at the end; he integrates it throughout. The first few chapters lay the foundations of vector spaces and matrices, but he immediately introduces geometric intuition. 2. The Geometric Product
Utilizing motors and rotors (more efficient than matrices). Applications: Practical examples in geometry and physics. Availability and Resources
Digital copies allow readers to quickly search for specific terms, formulas, or theorems across chapters.
: Generalizing the geometric product to arbitrary dimensions. Paving the way for geometric calculus, which replaces
5. Geometric Algebra 6. Linear Transformations 7. Representations 8. The Magical Conformal Model (added in the 4th printing) 9. Appendix
It covers traditional topics like vector spaces, linear transformations, and eigenvalues, but often with a focus on geometric interpretation.
If you are interested, I can also look for information about the author's other, related book, "Vector and Geometric Calculus," which is also highly regarded. Share public link
The book is structured to guide the reader logically from foundational concepts to advanced applications. If you share with third parties, their policies apply
The book is structured to guide readers from foundational linear algebra to advanced geometric concepts. Key areas covered include: Laying the foundation.
Alan Macdonald, Professor Emeritus of Mathematics at Luther College, developed this text to provide a for these areas, removing the need for diverse, separate techniques (like cross products, quaternions, or dual numbers, which are subsumed by GA). Key Features and Core Content
The physical and official digital copies of the textbook are available through standard academic book distributors and online retailers.