Just to align my thought, I’ll state the trivial.
Assume \boldsymbol{A} = \boldsymbol{C}^{T} \boldsymbol{C} for some matrix \boldsymbol{C}.
Mathematically \boldsymbol{A} is guaranteed to be SPSD. Yet numerical issues might cause it to have some small negative eigen values.
My idea is that using LDL Decomposition I will be able to clip the small negative values (I know the \boldsymbol{D} in LDL is not the \boldsymbol{D} in the Eigen Decomposition, just borrowed the concept).
So, given what’s available in Julia, is there a way to get the LDL of an SPSD matrix?