  We provide a description of the parity space reflection-time reversal (PT)
operator acting on the two-dimensional polarization space of light represented
by the linear algebra of Jones vectors and matrices. We establish the form of a
PT-symmetric Jones matrix. We present two examples of laser resonators whose
polarization eigenstates are described by PT-symmetric Jones matrices: one is
based on the Faraday effect and a dichroic attenuation, while the other is made
of twisted anisotropic mirrors. Both possess a control parameter that
experimentally covers the exact, the broken PT-symmetry regions and their
boundary, called an exceptional point, where the eigenstates of the resonator
coalesce into a single state. The exact PT-symmetric region produces laser
polarization modes emitting at the same frequency with different intracavity
losses, while the broken PT-symmetric region features polarization modes
emitting at distinct frequencies with the same intracavity losses. By applying
unitary transformations, the concept of PT-symmetric Jones matrix is extended
to matrices that commute with any antiunitary operator, thereby opening the
prospect of a larger family of resonators geometries that also feature real or
complex-conjugate spectra.
