Parametrization of the quark mixing matrix involving its eigenvalues

A parametrization of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix, $V$, is presented in which the parameters are the eigenvalues and the components of its eigenvectors. In this parametrization, the small departure of the experimentally determined $V$ from being moduli symmetric (i.e. $\mathrm{\mid }{V}_{ij}\mathrm{\mid }=\mathrm{\mid }{V}_{ji}\mathrm{\mid }$) is controlled by the small difference between two of the eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli symmetric $V$ depending on only three parameters. Our parametrization gives very good fits to the available data including CP-violation. Our value of $\sin 2\beta\approx 0.7$ and other parameters associated with the ` unitarity triangle’ $V_{11}{V}_{13}^{\ast }+V_{21}{V}_{23}^{\ast }{V}_{31}{V}_{33}^{\ast }=0$ are in good agreement with data and other analyses.