Grassmann–Cayley algebra
Script error: No such module "Labelled list hatnote".
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.Template:Refn It is the most general structure in which projective properties are expressed in a coordinate-free way.Template:Refn 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.Script error: No such module "Unsubst".
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.