  A parametrization of 3x3 unitary matrices is presented. This mathematical
approach is inspired on polarization algebra and is formulated through the
identification of a set of three orthonormal three-dimensional Jones vectors
representing the respective pure polarization states. This approach leads to
the representation of a 3x3 unitary matrix as an orthogonal similarity
transformation of a particular type of unitary matrix that depends on six
independent parameters, while the remaining three parameters correspond to the
orthogonal matrix of the said transformation. The results obtained are applied
to determine the structure of the second component of the characteristic
decomposition of a 3x3 positive semidefinite Hermitian matrix.
