Sweeping the Space of Admissible Quark Mass Matrices

We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to cover the general case, and of the polar decomposition theorem that allows to convert arbitrary nonsingular matrices to triangular form, we achieve a parameterization where the remaining freedom is reduced to one complex parameter. While this parameter runs through the domain bounded by a circle with radius R determined by the up-quark masses around the origin in the complex plane one sweeps the space of all mass matrices compatible with the given set of data.