Abstract
This chapter defines Geometric Algebra by a set of axioms and develops a system of definitions and identities to make it a versatile and efficient computational tool. These results are used repeatedly in subsequent chapters. Many results are obtained in the form of algebraic identities, but they are seldom presented as theorems, because we wish to emphasize the techniques for generating them, to show how a great variety of useful identities can be generated by a few simple techniques. For example, Section 1-4 shows how easily geometric algebra generates the system of identities making up the theory of determinants. Thus we can see the theory of determinants as only part of a more comprehensive algebraic system.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland
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Hestenes, D., Sobczyk, G. (1987). Geometric Algebra. In: Clifford Algebra to Geometric Calculus. Fundamental Theories of Physics, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6292-7_1
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DOI: https://doi.org/10.1007/978-94-009-6292-7_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-2561-5
Online ISBN: 978-94-009-6292-7
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