The principal argument for the adoption of geometric algebra is that it provides a single. A survey of geometric algebra and geometric calculus academics. I will illustrate this for linear algebra, vector calculus, real analysis, complex analysis, and several geometries. I will illustrate this for linear algebra, multivariable calculus, real analysis, complex analysis, and several geometries. Geometric algebra is an extension of linear algebra. Linear and geometric algebra alan macdonald download bok. This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the.
Geometric algebra sjsu scholarworks san jose state university. Linear and geometric algebra alan macdonald download. This section presents a powerful extension of this structure, the geometric algebra gn. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas, including linear algebra, multivariable calculus, real analysis, complex analysis, and euclidean, noneuclidean, and projective. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from.
He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The geometric algebra ga of a vector space is an algebra over a field, noted for its multiplication operation called the geometric product on a space of elements. Pdf linear and geometric algebra download full pdf. Algorithmic structure for geometric algebra operators and.
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. The treatment of many linear algebra topics is enhanced by geometric algebra. The treatment of many linear algebra topics is enhanced by geometric algebra, for example, determinants and orthogonal transformations. Macdonald 6, which includes geometric algebra alongside traditional linear algebra topics. The text is for the first undergraduate linear algebra course. It presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. David hestenes the principal argument for the adoption of geometric algebra is that. We can express any oriented length in r3 as a linear combination of the. Linear and geometric algebra by alan macdonald phd paperback.
A survey of geometric algebra and geometric calculus. Other members represent geometric operations on the geometric objects. In subsequent sections, we will explore the algebra and its applications. This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most. And geometric algebra does much more, as it incorporates the complex, quaternion, and exterior algebras, among others. Linear and geometric algebra by alan macdonald luther college.
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