Factorisation of a symmetric positive-definite matrix boldsymbolΣ = boldsymbolLboldsymbolL^T into a lower-triangular boldsymbolL. If boldsymbolZ sim mathcalN(boldsymbol0, boldsymbolI), then boldsymbolLboldsymbolZ sim mathcalN(boldsymbol0, boldsymbolΣ) — the standard recipe for correlated Gaussian samples in Monte Carlo. When boldsymbolΣ is only positive-semidefinite (rank-deficient, e.g. shrunk correlation matrices), Cholesky fails and one falls back on the eigendecomposition boldsymbolΣ = boldsymbolUboldsymbolLambdaboldsymbolU^T with boldsymbolL = boldsymbolUboldsymbolLambda^1/2.