[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.
[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.