I've read a number of tutorials on Clifford algebra, but I am still unsure of some elementary concepts.(adsbygoogle = window.adsbygoogle || []).push({});

For starters, how would I represent a vector in a 2D vector field as a Clifford multivector?

For 2D, a multivector is given by A = a0*1 + a1*e1+a2*e2 + a3*e1e2, where 1 is a scalar, e1 and e2 are vectors in the Clifford basis, and e1e2 is a bivector. If I had a vector (1,2) at position (3,4), what would its multivector be? I want to say

A = (3,4) + 1*e1 + 2*e2,

but I believe a0 needs to be a scalar, yet I don't see how else I would represent the (3,4) shift from the origin.

Second, suppose I miraculously found the Clifford algebra representation and did some operation that gave rise a multivector with contributions from the vector and bivector components (ie a0 through a3 are nonzero): in order to project back to Euclidean basis, would i merely retain only the a0 through a2 coefficients and set a3 to zero? Or must I do something to project the bivector component into the Euclidean space?

Thanks for your help!

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# Clifford algebra

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