affine transformations

In Jagannath and my project to fit dynamical models to streams in phase space, we have a simple problem, which is to take a diagonal covariance tensor for the noise in the observables (distances, angles, proper motions) and transform it, by the best first-order approximation, to a non-diagonal covariance tensor for the noise in the phase-space coordinates. This transformation is a bad idea because distance uncertainties plus the non-linear transformation take Gaussian noise in the observables to non-Gaussian noise in the phase-space coordinates. However, it is a very good idea because if we do this transformation and live with the inaccuracy it brings (it brings inaccuracy because we are treating the noise in phase space as Gaussian), our code becomes very fast! We are checking our math now (for the Nth time) and coding it up.