If you search for "Geometric Algebra PDF," you will find heavy hitters like Clifford Algebra to Geometric Calculus by Hestenes and Sobczyk (very advanced) or Geometric Algebra for Physicists by Doran and Lasenby (excellent but dense). Why choose Macdonald?
Traditional texts define the determinant via a messy cofactor expansion or Leibniz formula. Macdonald defines the determinant as the factor by which a linear transformation scales an oriented volume (via the outer product). This is the only definition that actually makes geometric sense. Alan Macdonald Linear And Geometric Algebra Pdf
Macdonald begins with standard linear algebra: vector spaces, linear transformations, determinants, and eigenvalues. However, even here, he emphasizes geometric intuition over rote calculation. He introduces the (wedge product) early, which sets the stage for the second half of the book. If you search for "Geometric Algebra PDF," you
Macdonald writes like a tutor sitting next to you. Every new concept is motivated by a problem in standard linear algebra. For example, he painfully demonstrates why the cross product fails in higher dimensions and how the wedge product fixes it immediately. Macdonald defines the determinant as the factor by
We hope this review has provided a helpful overview of Alan Macdonald's "Linear and Geometric Algebra" and the importance of these subjects in modern mathematics and physics.
