  It is shown that the Stokes-Mueller formalism can be reformulated in terms of
quaternions, and the quaternion approach is more suitable for the formalism of
Mueller-Jones states that we have recently described. In terms of quaternions
it can be shown that the vector and matrix states and the Jones matrix
associated to nondepolarizing optical systems are different representations
isomorphic to the same quaternion state, and this quaternion state turns out to
be the rotator of the Stokes quaternion. It is also shown that the coherent
linear combination of nondepolarizing optical media states and depolarization
phenomena can be reformulated in terms of quaternion states.
