平均因子分解法，适用于正定矩阵First, let s recall the definition of the Cholesky decomposition: Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U U, where U is the square root matrix of X, and satisfies:



(1) U U = X

(2) U is upper triangular (that is, it has all zeros below the diagonal).



It seems that the assumption of positive definiteness is necessary. Actually, it is "positive definite" which guarantees the existence of such kind of decomposition. -Average factor decomposition method applied to positive definite matrix First, let s recall the definition of the Cholesky decomposition: Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X = UU, where U is the square root matrix of X, and satisfies: (1) UU = X (2) U is upper triangular (that is, it has all zeros below the diagonal). It seems that the assumption of positive definiteness is necessary. Actually, it is　positive definite　which guarantees the existence of such kind of decomposition.