Measurement data processing using random matrices: a generalized formula for the propagation of uncertainty

In measurement practices, mathematical models and processing algorithms are often formulated in terms of transformations between matrices whose elements are measured quantities affected by uncertainty. In these cases, it is crucial to have a law for the propagation of the standard uncertainty valid for the estimation of the uncertainty and correlations in the results. In this paper, this formula will be derived, and some examples of its application to experimental measurement situations will be shown.