Grassmann–Cayley algebra

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Grassmann–Cayley algebra, also known as double algebra, is a form of modeling algebra for use in projective geometry.[1] 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.

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 kinesthetic analysis of manipulators.


  1. ^ Perwass, Christian (2009), Geometric algebra with applications in engineering, Geometry and Computing, 4, Springer-Verlag, Berlin, p. 115, ISBN 978-3-540-89067-6, MR 2723749 

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