  The application of high-resolution spectropolarimetry has led to major
progress in understanding the magnetism and activity of late-type stars. During
the last decade, magnetic fields have been discovered and mapped for many types
of active cool stars using spectropolarimetric data. However, these
observations and modeling attempts are fundamentally incomplete since they are
based on the interpretation of the circular polarization alone. Taking
advantage of the newly built HARPS polarimeter, we have obtained the first
systematic observations of several cool active stars in all four Stokes
parameters. Here we report the detection of magnetically-induced linear
polarization for the primary component of the very active RS CVn binary HR 1099
and for the moderately active K dwarf epsilon Eri. For both stars the amplitude
of linear polarization signatures is measured to be ~10^{-4} of the unpolarized
continuum, which is approximately a factor of ten lower than for circular
polarization. This is the first detection of the linear polarization in line
profiles of cool active stars. Our observations of the inactive solar-like star
alpha Cen A show neither circular nor linear polarization above the level of
10^{-5}, indicating the absence of a net longitudinal magnetic field stronger
than 0.2 G.
