Why Geometric Algebra Should be in the Standard Linear Algebra Curriculum by Logan Lim

For more information on the seminar, see: pgadey.ca/semi....
Abstract:
Geometric algebra is an extension of R^n that includes as special cases: The complex numbers, quaternions, exterior algebras, dual numbers, split-complex numbers, dual quaternions and more! When applied to multivariable calculus, it generalizes the fundamental theorem of calculus on manifolds to include the divergence theorem, curl theorem, and gradient theorem, and as a result Green’s and Stoke’s theorem, as special cases of a single statement. It also simplifies many geometric operations in computer graphics by eliminating the need for matrices in projections, rotations, and reflections. Though we can only cover the ‘main idea’ of geometric algebra in the allotted time, this talk will be a buffet of ideas you can explore for this fascinating and deceptively simple algebraic object.
#MTBoS #geometricalgebra #bivector #quaternions #complexnumbers #grassmann #clifford