masses are necessarily sub-dominant. To see this explicitly, consider only the left handed canonical normalisation $N_{ik}$ with $N$ upper triangular. Now using Eq. (\[totYuk\]) the canonical Yukawa and the fact that the Yukawa and Kähler matrices are hierarchical in the left handed sector, the determinant of $Y^{t}$ is, $$\mbox{Det}(Y^{t})=\mbox{Det}(N)\mbox{Det}(\hat{Y})\simeq (1+{\mathcal{O}}(\leq \epsilon ))\mbox{Det}(\hat{Y})$$Moreover, from the hierarchical structure in Eq. (\[genform\]) we know that any element of the matrix is corrected only at ${\mathcal{O}}(\leq
\epsilon ^{2})$ under the transformations to canonical left-handed Kähler. In particular, the heaviest eigenvalue in $Y^{t}$ will be still be $1+{\mathcal{O}}(\leq \epsilon ^{2})$. Therefore this implies that the product of the two lightest eigenvalues can only be changed at ${\mathcal{O}}(\leq
\epsilon ^{2})$. Finally the second eigenvalue is basically obtained from the lightest eigenvalue of the $(2,3)$ submatrix and thus we obtain again that any change to this eigenvalue will be sub-dominant in $\epsilon $ and therefore the same is true for the first generation eigenvalue.

In the case of a non-hierachical structure in the $(2,3)$ entry with $N_{23}^{R}$ of ${\mathcal{O}}(1)$ we expect $\mbox{Det}(N^{R})$ to be ${\mathcal{O}}(1)$ barring accidental cancellations. In this case the corrections to the eigenvalues, while still not changing their order in $\epsilon ,$ could be 