  In this work we derive a matrix formulation of a noise-disturbance
uncertainty relation, which is akin to the Robertson-Schr\"odinger uncertainty
principle. Our inequality is stronger than Ozawa's uncertainty principle and
takes noise-disturbance correlations into account. Moreover, we show that, for
certain types of measurement interactions, it is covariant with respect to
linear symplectic transformations of the noise and disturbance operators.
