Alan Macdonald’s Linear and Geometric Algebra is a forward-thinking textbook that bridges the gap between standard, dry linear algebra and the elegant, powerful world of Geometric Algebra. By fostering both algebraic proficiency and geometric intuition, it prepares students for modern engineering and physics problems.
Introduction to vectors, the outer product, and bivectors in two dimensions.
Alan Macdonald maintains an academic homepage through Luther College. He frequently provides complementary materials, errata sheets, chapter supplements, and software code directory links directly to the public. alan macdonald linear and geometric algebra pdf
Macdonald organizes the material into three main sections: , Geometric Algebra , and Linear Transformations . Highlights Traditional Foundations
CreateSpace Independent Publishing Platform (2011) ISBN-13: 978-1453854938 Level: Undergraduate (junior/senior) — requires calculus but no prior linear algebra. Alan Macdonald’s Linear and Geometric Algebra is a
By combining these two concepts, the geometric product is invertible, a property that standard vector algebra lacks. 2. Blades and Multivectors
Standard topics like vector spaces, matrices, linear independence, and inner product spaces. Alan Macdonald maintains an academic homepage through Luther
Once the algebra of lines and areas is mastered, the author's sequel, Vector and Geometric Calculus , extends these principles to derivatives and integrals. This ultimately unifies foundational mathematical theorems (Stokes's, Gauss's, and the Fundamental Theorem of Calculus) into a single, beautiful identity.
Investing time in Macdonald's text equips students with a cutting-edge mathematical toolset that simplifies higher-level physics, engineering, and geometry.
Pioneered in the 1960s by physicist David Hestenes, Geometric Algebra extends classical linear algebra by introducing a new operation: the . While the standard dot product yields a scalar and the cross product (applicable only in 3D) yields a perpendicular vector, the geometric product allows you to multiply vectors together to create new geometric entities.