Clifford algebra
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In mathematics, Clifford algebras are a type of associative algebra. As K-algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems.
Description
The theory of Clifford algebras is intimately connected with the theory of quadratic forms and orthogonal transformations.
Clifford algebras have important applications in a variety of fields including geometry, theoretical physics and digital image processing.
They are named after the English geometer William Kingdon Clifford.
The most familiar Clifford algebra, or orthogonal Clifford algebra, is also referred to as Riemannian Clifford algebra.
See also
- Algebra of physical space, APS
- Cayley–Dickson construction
- Classification of Clifford algebras
- Clifford analysis
- Clifford module
- complex spin structure
- Dirac operator
- Exterior algebra
- Gamma matrices
- Generalized Clifford algebra
- Geometric algebra
- Higher-dimensional gamma matrices
- hypercomplex number
- Octonion
- Paravector
- quaternion
- Spin group
- Spin structure
- Spinor
- spinor bundle
External links
- Clifford algebra @ Wikipedia.org
