  We introduce a nonsymmetric real matrix which contains all the information
that the usual Hermitian density matrix does, and which has exactly the same
tensor product structure. The properties of this matrix are analyzed in detail
in the case of multi-qubit (e.g. spin = 1/2) systems, where the transformation
between the real and Hermitian density matrices is given explicitly as an
operator sum, and used to convert the essential equations of the density matrix
formalism into the real domain.
