Let A be a real element 4 x 4 Mueller matrix given as fa11 a12 a,a a4 a21 az2 az3 a24 A = a31 a32 a33 a34 La1 a42 a4a as Construct the covariance matrix B(A) such that the elements b, of the matrix B(A) can be written directly in terms of the elements a, such that 1 B(A) =, a, E., J=1 Where E, are the 16 modified Dirac matrices. (See Arfken), which in turn can be written in terms of the Pauli spin matrices such that E, = o, O 0,. Where O denoting the tensor product. The Pauli matrices are