This article shows that only polarizers, retarders, and improper rotat
ion Mueller matrices do not decrease the degree of polarization for an
y input Stokes vector. On the other hand, a Mueller matrix does not in
crease the degree of polarization for any input Stokes vector if and o
nly if it has an unpolarized Stokes vector as eigenvector. Furthermore
, for any Mueller matrix an unpolarized incident Stokes vector always
has the maximum gain in the degree of polarization. It is pointed out
that a general Mueller matrix deforms the Poincare sphere (for input S
tokes vectors) into an ellipsoid (for output Stokes vectors). Finally,
several inequalities involving the input and output degrees of polari
zation are derived. (C) 1998 Published by Elsevier Science B.V.