  Let $H$ be any $\PT$ symmetric Schr\"odinger operator of the type $
-\hbar^2\Delta+(x_1^2+...+x_d^2)+igW(x_1,...,x_d)$ on $L^2(\R^d)$, where $W$ is
any odd homogeneous polynomial and $g\in\R$. It is proved that $\P H$ is
self-adjoint and that its eigenvalues coincide (up to a sign) with the singular
values of $H$, i.e. the eigenvalues of $\sqrt{H^\ast H}$. Moreover we
explicitly construct the canonical expansion of $H$ and determine the singular
values $\mu_j$ of $H$ through the Borel summability of their divergent
perturbation theory. The singular values yield estimates of the location of the
eigenvalues $\l_j$ of $H$ by Weyl's inequalities.
