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math.GM2018
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…
math.GM2018
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,…
math.GM2018
From Vectors to Geometric Algebra
Sergio Ramos Ramirez, Jose Alfonso Juarez Gonzalez, Garret Sobczyk
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of ve…