For a vector space with quadratic form , its Clifford algebra is generated by vectors subject to . In a basis this is equivalently .
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Clifford algebra is a mathematical structure that extends the concept of vector spaces and inner products into a more generalized algebraic framework. It is named after the mathematician William Kingdon Clifford, who developed the concept in the 19th century. ### Definition A Clifford algebra is generated from a vector space \( V \) equipped with a quadratic form.