A complete and minimum set of necessary and sufficient conditions for a real 4 x 4 matrix to be a physical Mueller matrix is obtained. An additional condition is presented to complete the set of known conditions, namely, the four conditions obtained from the nonnegativity of the eigenvalues of the Hermitian matrix H associated with a Mueller matrix M and the transmittance condition. Using the properties of H, a demonstration is also presented of Tr((MM)-M-T) = 4m(00)(2) as being a necessary and sufficient condition for a physical Mueller matrix to be a pure Mueller matrix. (C) 2000 Optical Society of America [S0740-3232(00)01702-6] OCIS codes: 260.5430, 120.2130.
