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Geometric algebra (along with an associated Geometric calculus, Spacetime algebra and Conformal Geometric algebra, together GA) provides an alternative and comprehensive approach to the algebraic representation of classical, computational and relativistic geometry. GA now finds application in all of Physics, in graphics, robotics as well as the mathematics of its formal parents, the Grassmann and Clifford algebras.
A distinguishing characteristic of GA is that its products are used and interpreted geometrically due to the natural correspondence between geometric entities and the elements of the algebra. GA allows one to manipulate subspaces directly and is a coordinatefree formalism.
Proponents argue it provides compact and intuitive descriptions in many areas including classical and quantum mechanics, electromagnetic theory and relativity among others. They strive to work with real algebras wherever that is possible and they argue that it is generally possible and usually enlightening to identify the presence of an imaginary unit in a physical equation. Such units arise from one of the many quantities in the real algebra that square to 1, and these have geometric significance because of the properties of the algebra and the interaction of its various subspaces.
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