  We observe the slowly-rotating, active, single giant, EK Eri, to study and
infer the nature of its magnetic field directly. We used the spectropolarimeter
NARVAL at the Telescope Bernard Lyot, Pic du Midi Observatory, and the Least
Square Deconvolution method to create high signal-to-noise ratio Stokes V
profiles. We fitted the Stokes V profiles with a model of the large-scale
magnetic field. We studied the classical activity indicators, the CaII H and K
lines, the CaII infrared triplet, and H\alpha line. We detected the Stokes V
signal of EK Eri securely and measured the longitudinal magnetic field Bl for
seven individual dates spanning 60% of the rotational period. The measured
longitudinal magnetic field of EK Eri reached about 100 G and was as strong as
fields observed in RSCVn or FK Com type stars: this was found to be
extraordinary when compared with the weak fields observed at the surfaces of
slowly-rotating MS stars or any single red giant previously observed with
NARVAL. From our modeling, we infer that the mean surface magnetic field is
about 270 G, and that the large scale magnetic field is dominated by a poloidal
component. This is compatible with expectations for the descendant of a
strongly magnetic Ap star.
