Random numbers, correlated

The notion of correlation is linked with that of variance and elements in an error matrix. Correlated random numbers arise from uncorrelated random numbers by error propagation. If correlated random numbers have to be generated according to a known error matrix, the inverse operation (of error propagation) is required: what is wanted is the matrix A which transforms the unit matrix I into the (given) error matrix E when propagating errors, viz. File:Hepa img900.gif . This is exactly the problem of Cholesky decomposition: A will be a triangular matrix, and it can be found from E by that comparatively simple algorithm.