We know that a positive deﬁnite matrix has a Cholesky decomposition,but I want to know how a Cholesky decomposition can be done for positive semideﬁnite matrices?The following sentences come from a paper. "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 semideﬁniteness directly, as we do a Cholesky decomposition of the matrix R at the very start. If R is not positive semideﬁnite, the Cholesky decomposition will fail." Thank you for your answer.
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