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Spheroidal Domains and Geometric Analysis in Euclidean Space
Garret Sobczyk
Clifford's geometric algebra has enjoyed phenomenal development over the last 60 years by mathematicians, theoretical physicists, engineers and computer scientists in robotics, art…
Nested Coordinate Systems in Geometric Algebra
Garret Sobczyk
A nested coordinate system is a reassigning of independent variables to take advantage of geometric or symmetry properties of a particular application. Polar, cylindrical and spher…
Periodic Table of Geometric Numbers
Garret Sobczyk
Perhaps the most significant, if not the most important, achievements in chemistry and physics are the Periodic Table of the Elements in Chemistry and the Standard Model of Element…
What's in a Pauli Matrix?
Garret Sobczyk
Why is it that after so many years matrices continue to play such an important roll in Physics and mathematics? Is there a geometric way of looking at matrices, and linear transfor…
Notes on Plucker's relations in Geometric Algebra
Garret Sobczyk
Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up utilizing using many different lan…
Geometric Matrices and the Symmetric Group
Garret Sobczyk
We construct real and complex matrices in terms of Kronecker products of a Witt basis of 2n null vectors in the geometric algebra over the real and complex numbers. In this basis,…