Linear and Geometric Algebra

by Alan MacDonald

This textbook for the first undergraduate linear algebra course presents a unified treatment of linear algebra and geometric algebra, while covering most of the usual linear algebra topics. Geometric algebra is an extension of linear algebra. It enhances the treatment of many linear algebra topics. And geometric algebra does much more. Geometric algebra and its extension to geometric calculus unify, simplify, and generalize vast areas of mathematics that involve geometric ideas. They provide a unified mathematical language for many areas of physics, computer science, and other fields. The book can be used for self study by those comfortable with the theorem/proof style of a mathematics text. This is a second printing, corrected and slightly revised. Visit the book's web site for more information: http: //faculty.luther.edu/ macdonal/laga I commend Alan Macdonald for his excellent book! His exposition is clean and spare. He has done a fine job of engineering a gradual transition from standard views of linear algebra to the perspective of geometric algebra. The book is sufficiently conventional to be adopted as a textbook by an adventurous teacher without getting flack from colleagues. Yet it leads to gems of geometric algebra that are likely to delight thoughtful students and surprise even the most experienced instructors. -- David Hestenes, Distinguished Research Professor, Arizona State University

Genres: Mathematics, Textbooks, Stem

224 pages, Paperback

First published January 19, 2011

Reviews

[Mark Moon · Rating 5 out of 5]

Very nice.

[Lucille Nguyen · Rating 3 out of 5]

I read this book because I read Arjun Mani's "Representing Words in a Geometric Algebra" and was fascinated in better understanding the notation. This book was okay, provided a decent overview of linear algebra and a smattering of geometric algebra. The position of definition and explanation gave much to be desired. Eric Lengyel wrote an interesting piece here (https://terathon.com/blog/ga-books.html) arguing that MacDonald misdefined the contractions, inner products, and duals in this work. Will read more books on the subject to evaluate.

[Jacob · Rating 5 out of 5]

Excellent introduction to the topic.

[Lorraine Weis · Rating 4 out of 5]

Straight forward introduction to Geoemetric algebra, for people who are comfortabler with mathematical language. While it also gives a good, clear foundation for linear algebra, the language is probably a little dense for most lower level undergrad classes.