the rotation away from being diagonal matrices just a coordinate transformation away from being diagonal so we can just as well think of it as diagonal matrices if we were just working the correct coordinate system okay so imagine it's diagonal then we really see like x1 and mu1 attracting with the first entry in that diagonal and x2 mutant with the second entry and completely independent no interaction so x1 and x2 are their own gaussians in that coordinate system where now they might have different variances because the