  We construct real and complex matrices in terms of Kronecker products of a
Witt basis of 2n null vectors in the geometric algebra over the real and
complex numbers. In this basis, every matrix is represented by a unique sum of
products of null vectors. The complex matrices provide a direct matrix
representation for geometric algebras with signatures p+q <= 2n+1. Properties
of irreducible representations of the symmetric group are presented in this
geometric setting.
