Robertson-Schr\"odinger formulation of Ozawa's Uncertainty Principle

A more general measurement disturbance uncertainty principle is presented in a Robertson-Schr"odinger formulation. It is shown that it is stronger and having nicer properties than Ozawa’s uncertainty relations. In particular is invariant under symplectic transformations. One shows also that there are states of the probe (measuring device) that saturate the matrix formulation of measurement disturbance uncertainty principle.