# Projecting matrix from LDL^T factorization

When factorizing a real symmetric matrix $$A$$ into $$LDL^T$$, the matrix $$D$$ can have 1x1 or 2x2 blocks on the diagonal. A condition for $$A$$ to be positive-definite is that all 1x1 and 2x2 blocks of $$D$$ are positive-definite.

As in this question, I would like to know it would be possible to project $$A$$ into its positive-eigenvalue subspace from its $$LDL^T$$ factorization.

For example, I am wondering if defining $$D'$$ by replacing all non-positive blocks of $$D$$ by 0 would result in this projection for $$A' = LD'L^T$$.