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In mathematics, a Clifford algebra^[a] is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished subspace. As $K$ -algebras, they generalize the real numbers, complex numbers, quaternions and several other hypercomplex number systems.^[1]^[2] 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 mathematician William Kingdon Clifford (1845–1879).

The most familiar Clifford algebras, the orthogonal Clifford algebras, are also referred to as (pseudo-)Riemannian Clifford algebras, as distinct from symplectic Clifford algebras.^[b]

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^ Clifford 1873, pp. 381–395
^ Clifford 1882