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We obtain constraints on possible structures of mass matrices in the quarksector by using as experimental restrictions the determined values of the quarkmasses at the $M_Z$ energy scale, the magnitudes of the quark mixing matrixelements $V_{\rm ud}$, $V_{\rm us}$, $V_{\rm cd}$, and $V_{\rm cs}$, and theJarlskog invariant $J(V)$. Different cases of specific mass matrices areexamined in detail. The quality of the fits for the Fritzsch and Stech typemass matrices is about the same with $\chi^2/{\rm dof}=4.23/3=1.41$ and$\chi^2/{\rm dof}=9.10/4=2.28$, respectively. The fit for a simplegeneralization (one extra parameter) of the Fritzsch type matrices, in thephysical basis, is much better with $\chi^2/{\rm dof}=1.89/4=0.47$. Forcomparison we also include the results using the quark masses at the 2 GeVenergy scale. The fits obtained at this energy scale are similar to that at$M_Z$ energy scale, implying that our results are unaffected by the evolutionof the quark masses from 2 to 91 GeV.

Bounds on quark mass matrices elements due to measured properties of the mixing matrix and present values of the quark masses