Grassmann–Cayley algebra

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In mathematics, a Grassmann–Cayley algebra is the exterior algebra with an additional product, which may be called the shuffle product or the regressive product.[1] It is the most general structure in which projective properties are expressed in a coordinate-free way.[2] The technique is based on work by German mathematician Hermann Grassmann on exterior algebra, and subsequently by British mathematician Arthur Cayley's work on matrices and linear algebra. It is a form of modeling algebra for use in projective geometry.[citation needed]

The technique uses subspaces as basic elements of computation, a formalism which allows the translation of synthetic geometric statements into invariant algebraic statements. This can create a useful framework for the modeling of conics and quadrics among other forms, and in tensor mathematics. It also has a number of applications in robotics, particularly for the kinematical analysis of manipulators.


  1. ^ Perwass, Christian (2009), Geometric algebra with applications in engineering, Geometry and Computing, vol. 4, Springer-Verlag, Berlin, p. 115, ISBN 978-3-540-89067-6, MR 2723749
  2. ^ Hongbo Li; Olver, Peter J. (2004), Computer Algebra and Geometric Algebra with Applications: 6th International Workshop, IWMM 2004, GIAE 2004, Lecture Notes in Computer Science, vol. 3519, Springer, ISBN 9783540262961

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