Orthonormal Basis Sets in Clifford Algebras

Orthonormal basis sets define isomorphisms and automorphisms in Clifford algebras. Orthonormal basis sets (ONB) are defined as sets of multivectors satisfying scalar product relations. A FORTRAN program determining ONBs is described. It is shown that any simple Clifford algebra is isomorphic to the tensor product of a Clifford algebra Cℓ m,m and a Clifford algebra isomorphic to ℝ, ℂ or ℍ. From the construction of matrix algebras isomorphic to Cℓ m,m given by the second FORTRAN program, matrix algebras with entries in ℝ, ℂ or ℍ can be used to construct isomorphisms to all simple Clifford algebras.