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A parametrization of 3x3 unitary matrices is presented. This mathematicalapproach is inspired on polarization algebra and is formulated through theidentification of a set of three orthonormal three-dimensional Jones vectorsrepresenting the respective pure polarization states. This approach leads tothe representation of a 3x3 unitary matrix as an orthogonal similaritytransformation of a particular type of unitary matrix that depends on sixindependent parameters, while the remaining three parameters correspond to theorthogonal matrix of the said transformation. The results obtained are appliedto determine the structure of the second component of the characteristicdecomposition of a 3x3 positive semidefinite Hermitian matrix.

Parametrization of 3x3 unitary matrices based on polarization algebra