In a numerical implementation, it is helpful to express the result in terms of the Cholesky decompositions L 0 , L 1 such that Σ Σ 0 = L 0 L 0 T and Σ Σ 1 = L 1 L 1 T . Then with M and y solutions to the triangular linear systems L 1 M = L 0 , and L 1 y = μ μ 1 − − μ μ 0 ,