I know I'm not the first to do this and I can't find what it's called that would tell me how to solve for $L$ when $X$ is a symmetric positive semidefinite. I know
orth(A)*transpose(orth(A)) = [Identity matrix]
and
[q,r]=qr(A)
q*r == A
but I can't find $X = LL^T$. If anyone knows what the method is named/called that I could use to solve this it'd be really appreciated!
You're looking for Cholesky Factorization.