Neutrino mass matrix: inverted hierarchy and CP violation

We reconstruct the neutrino mass matrix in flavor basis, in the case of inverted mass hierarchy (ordering), using all available experimental data on neutrino masses and oscillations. We analyze the dependence of the matrix elements m_{alpha beta} on the CP violating Dirac, delta, and Majorana, rho and sigma, phases, for different values of the absolute mass scale. We find that the present data admit various structures of the mass matrix: (i) hierarchical structures with a set of small (zero) elements; (ii) structures with equalities among various groups of elements: e-row and/or mu tau-block elements, diagonal and/or off-diagonal elements; (iii) ``democratic'' structure. We find values of phases for which these structures are realized. The mass matrix elements can anti-correlate with flavor: inverted partial or complete flavor alignment is possible. For various structures of the mass matrix we identify possible underlying symmetry. We find that the mass matrix can be reconstructed completely only in particular cases, provided that the absolute scale of the mass is measured. Generally, the freedom related to the Majorana phase sigma will not be removed, thus admitting various types of mass matrix