Cholesky Decomposition

See this PDF file for the R script.

See this MS-Excel file for a case of manual calculation.

Cholesky decomposition is only valid for positive definite matrix.
It may be used to test if a matrix is positive definite.
NONMEM use this for the transformation of omega and sigma matrix into unconstrained parameter (UCP). UCP is previously called STP(scaled transformed parameter).
For the inversion of hessian or linear system solution, LDL' transformation is more useful.
During the minimization process we cannot guarantee that hessian matrix is positive definite but which is always symmetric.
LDL' transformation can be used always for any real symmetric matrix.