Thank you for your answer.In Matlab Programming, the "chol" command can be used to simply apply this to only a positive definite matrix.When it comes to a positive semi-definite matrix，“chol” fails.I want to ask if there any command in Matlab Programming that can be used to a positive semi-definite matrix?

In Matlab Programming, the "chol" command can be used to simply apply this to only a positive definite matrix.When it comes to a positive semi-definite matrix，“chol” fails.I want to ask if there any command in Matlab Programming that can be used to a positive semi-definite matrix?

Thank you for your answer.But when R is a positive definite matrix,is there any method to do a Cholesky decomposition for R?For example,in the tool of MATLAB,we know that the instruction of chol can do a Cholesky decomposition when R is a positive definite matrix.

It is no doubt that R has a Cholesky decomposition when R is a positive definite matrix.I want to ask Whether R has a Cholesky decomposition when R is a positive semi-definite?Thank you for your patience~~

excuse for my bad english."There are two assumptions on the specified correlation matrix R. The first is a general assumption that R is a possible correlation matrix, i.e. that it is a symmetric positive semidefinite matrix with 1’s on the main diagonal. While implementing the algorithm there is no need to check positive semi-definiteness directly, as we do a Cholesky decomposition of the matrix R at the very start. If R is not positive semi-definite, the Cholesky decomposition will fail."

THANK YOU .but here I want to know if a positive semi-definite can be done for Cholesky decomposition? and how?