Synonyms
Definition
Geometric algebra is an algebra based on a geometric product of vectors in an inner product space (a.k.a. the Clifford product). It naturally extends common geometrical techniques from linear algebra, to process subspaces and operations between them in a direct, coordinate-free manner. It permits division by subspaces (notably vectors), which leads to much more compact expression of common operations and algorithms in linear algebra, and more direct solutions to equations. Geometric algebra includes quaternions, in a real construction as a ratio of vectors, and extends them to encode rigid body motions. Geometric algebra also extends vector calculus to permit direct differentiation with respect to geometrical quantities and operators, thus allowing classically scalar optimization techniques to be transferred directly to geometric settings.
Background
Geometric algebra (GA) (or Clifford algebra) and its predecessor Grassmann algebra date from the...
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Dorst, L. (2014). Geometric Algebra. In: Ikeuchi, K. (eds) Computer Vision. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-31439-6_656
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DOI: https://doi.org/10.1007/978-0-387-31439-6_656
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