In reply to Spencer Wadsworth.

> I was wondering if you knew of a source such as a standard textbook which gives the Cholesky decomposition result you showed

I'm not sure which "result" you are referring to. If you are referring to the matrix equation after the phrase "the Cholesky decomposition of $\Sigma$ can be written in block form as", that identity is true by inspection. Just multiply the factors to obtain the block for of \Sigma. If you are referring to the L*D*L` decomposition, you can refer to Golub and Van Loan "Matrix Computations" (2nd Ed), p. 137-138.