Grassmann–Cayley algebra
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.
References
- ↑ Perwass, Christian (2009), Geometric algebra with applications in engineering, Geometry and Computing, 4, Springer-Verlag, Berlin, p. 115, ISBN 978-3-540-89067-6, Bibcode: 2009gaae.book.....P, https://books.google.com/books?id=8IOypFqEkPMC&pg=PA115
- ↑ 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, 3519, Springer, ISBN 9783540262961, https://books.google.com/books?id=q68fUw31mrkC&pg=PA387
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