: Covers fundamental topics such as vectors, vector spaces, matrices, and inner product spaces. Part II: Geometric Algebra
It replaces disparate concepts (like Gibbs' cross product in 3D, complex numbers in 2D, and quaternions in 4D) with a single geometric language applicable to any dimension.
The cornerstone of the book is the geometric product of two vectors , defined as:
Macdonald’s textbook completely rethinks standard undergraduate linear algebra by introducing the early on. Instead of treating determinants, cross products, and complex numbers as separate entities, the book unifies them using the following foundational elements: 1. The Geometric Product alan macdonald linear and geometric algebra pdf
Introducing the inner and outer products.
Scope and purpose
: Generalizing the geometric product to arbitrary dimensions. : Covers fundamental topics such as vectors, vector
Before diving into the PDF, it is crucial to understand the author. Alan Macdonald is a Professor Emeritus of Mathematics at Luther College in Decorah, Iowa. Unlike many mathematicians who write in dense, theorem-proof formats, Macdonald comes from a pedagogical tradition. His life’s work has been dedicated to making advanced mathematics accessible to undergraduates.
, this paper is specifically designed to be an accessible entry point for anyone with a background in undergraduate mathematics. Luther College Key Resources A Survey of Geometric Algebra and Geometric Calculus
CreateSpace Independent Publishing Platform (2011) ISBN-13: 978-1453854938 Level: Undergraduate (junior/senior) — requires calculus but no prior linear algebra. Before diving into the PDF, it is crucial
If you are just beginning to explore the intersection of these mathematical concepts, there are multiple ways to tailor your learning experience.
If you want, I can:
), where complex numbers and quaternions are revealed as natural parts of the algebra.