Matrix representations of Clifford algebras (Q915824)

It is well-known that Clifford algebras can be faithfully realized as certain matrix algebras, the matrix entries being real numbers, complex numbers, or quaternions, depending on the particular Clifford algebra. One shows that the matrix representations of the basis elements of a Clifford algebra can be chosen to satisfy a certain additional trace condition; this trace condition is used to establish optimal inequalities involving norms in Clifford algebras.