Constraints on mass matrices due to measured property of the mixing matrix

It is shown that two specific properties of the unitary matrix V can be expressed directly in terms of the matrix elements and eigenvalues of the hermitian matrix M which is diagonalized by V. These are the asymmetry Delta(V) = vertical bar V-12 vertical bar(2) - vertical bar V-21 vertical bar(2), of V with respect to the main diagonal and the Jarlskog invariant J(V) = Im(V11V*V-12*(21), V-22). These expressions for Delta(V) and J(V) provide constraints on possible mass matrices from the available data on V.