Please provide detailed proof.
7. Let k and l be positive integers, and set n:= k + l. Suppose A <- C^nxn has the decomposition
A = | B C^H |
| C D |,
where B <- C^kxk, B <- C^lxk, and D <- C^lxl.
(a) If A is HPD, prove that B, D and E :: D - (C B^-1 C^H) are HPD. E is called the Schur compliment of B in A.
(b) Suppose A is HPD. Express the Cholesky factorization of A in terms of the Cholesky factorizations of B, D, and E.© BrainMass Inc. brainmass.com March 21, 2019, 10:51 pm ad1c9bdddf
This solution shows step-by-step workings to contextualize the Cholesky Decomposition.