  Production and decay angular distributions were extracted from measurements
of exclusive electroproduction of the rho^0(770) meson over a range in the
virtual photon negative four-momentum squared 0.5< Q^2 <4 GeV^2 and the
photon-nucleon invariant mass range 3.8< W <6.5 GeV. The experiment was
performed with the HERMES spectrometer, using a longitudinally polarized
positron beam and a ^3He gas target internal to the HERA e^{+-} storage ring.
The event sample combines rho^0 mesons produced incoherently off individual
nucleons and coherently off the nucleus as a whole. The distributions in one
production angle and two angles describing the rho^0 -> pi+ pi- decay yielded
measurements of eight elements of the spin-density matrix, including one that
had not been measured before. The results are consistent with the dominance of
helicity-conserving amplitudes and natural parity exchange. The improved
precision achieved at 4< W <7 GeV, in combination with other data at W>7 GeV,
reveals evidence for an energy dependence in the ratio R of the longitudinal to
transverse cross sections at constant Q^2.
