Clifford module
In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field K over which the quadratic form Q defining C is defined.
The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature p − q (mod 8). This is an algebraic form of Bott periodicity.
We will need to study anticommuting matrices (AB = −BA) because in Clifford algebras orthogonal vectors anticommute
For the real Clifford algebra , we need p + q mutually anticommuting matrices, of which p have +1 as square and q have −1 as square.
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