You will learn to multiply two vectors to get a complex number-like entity (a spinor). You will prove that $v^2 = |v|^2$ (a scalar) and that for orthogonal vectors, $ab = -ba$ (anti-commutativity). This reveals why complex numbers and quaternions are just subsets of geometric algebra.
Linear and geometric algebra have numerous applications in modern mathematics and physics. Some of the key areas where these subjects are used include: Alan Macdonald Linear And Geometric Algebra Pdf
– Contrasting Macdonald’s approach with Strang, Axler, and Hestenes. You will learn to multiply two vectors to
(This introduction sets the stage. The essay would continue with sections on:) Linear and geometric algebra have numerous applications in
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.