Euclidean 3D Geometric Algebra (Cl3)
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Generally, a multivector in Cl3 can be rewritten aswhere for vectors and complex vectors we are using the bold format here. We have already seen that the unit pseudoscalar j commutes with all elements of the algebra and squares to −1, and therefore, it is an ideal replacement for the ordinary imaginary unit (there are many “imaginary units” in GA). A pseudoscalar with such properties will appear again in Cl7, Cl11, … (see E10). Here we often use a very useful form of a multivector:
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