 The actual linear dependencies in formula_6 and formula_42 are remarkable and they are in both cases the best one can hope for in this kind of algorithm.Yet, a rigorous proof of convergence is missing.Using a non-identity covariance matrix for the multivariate normal distribution in evolution strategies is equivalent to a coordinate system transformation of the solution vectors, mainly because the sampling equation

can be equivalently expressed in an "encoded space" as 

The covariance matrix defines a bijective transformation (encoding) for all solution vectors into a space, where the sampling takes place with identity covariance matrix.