  For a general-form polarization biphoton qutrit, physically corresponding to
a pair of arbitrarily polarized photons in a single frequency and wavevector
mode, we explicitly find polarization Schmidt modes. A simple method is
suggested for factorizing the state vector and the explicit expressions for the
factorizing photon creation operators are found. The degrees of entanglement
and polarization of a qutrit are shown to depend directly on the commutation
features of the factorizing operators. Clear graphic representations for the
Stokes vectors of the qutrit state as a whole, its Schmidt modes, and
factorizing single-photon creation operators are given, based on the Poincar\'e
sphere. An experimental scheme is proposed for measuring the parameters of the
Schmidt decomposition as well as for demonstrating the operational meaning of
qutrit entanglement.
