Geometric algebra, exact and least squares solutions of two variable linear system
Peeter's math and physics play
In this video, we use a 2 parameter linear system to show how wedge products can be used to solve exact linear systems. We see how this relates to Cramer's rule, and see how to generalize the solution method to inexact systems, solving the least squares problem geometrically. Finally, we use a conventional calculus least squares formulation, and show that this leads to the same solution as the geometric algebra formulation.
Numerical examples are shown using a mathematica notebook that can be found in:
https://github.com/peeterjoot/mathematica/blob/master/blogit/ga30_wedge_solution.nb
This example uses the GA30 mathematica module available from git@github.com:peeterjoot/gapauli.git
Prerequisites: geometric algebra basics (vector multiplication, grade selection, vector/bivector products, bivector products and dot products, ...), linear algebra (matrix algebra, inversion, ...), and calculus (partial differentials, minimization.)
Wordpress and PDF versions of this video can be found at:
If you liked this material you may be interested in my blog:
or my book (Geometric Algebra for Electrical Engineers), which is available for free in pdf form at:
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