I get the cholesky-factor C by the LDU-decomposition as $\small C=L\cdot D$ with
$ \small \text{L=}\begin{bmatrix} 1&0&0&0&0&0&0&0&0\\ -1/2&1&0&0&0&0&0&0&0\\ 0&-2/5&1&0&0&0&0&0&0\\ -1/2&-1/5&-1/8&1&0&0&0&0&0\\ 0&-2/5&-1/4&-10/19&1&0&0&0&0\\ 0&0&-5/8&-1/19&-25/54&1&0&0&0\\ 0&0&0&-8/19&-5/27&-16/95&1&0&0\\ 0&0&0&0&-19/54&-5/19&-15/17&1&0\\ 0&0&0&0&0&-54/95&-2/17&-1&1 \end{bmatrix} $
and the diagonalmatrix D with $ \small \text{diag(D)=} \begin{bmatrix} \sqrt{2}&\sqrt{5/2}&\sqrt{8/5}&\sqrt{19/8}&\sqrt{54/19}&\sqrt{95/54}&\sqrt{136/95}&\sqrt{24/17}& 0 \end{bmatrix} $
Numerically to two dec digits this is
$ \small \text{ C =} \begin{bmatrix} 1.41& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00\\ -0.71& 1.58& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00\\ 0.00& -0.63& 1.26& 0.00& 0.00& 0.00& 0.00& 0.00& 0.00\\ -0.71& -0.32& -0.16& 1.54& 0.00& 0.00& 0.00& 0.00& 0.00\\ 0.00& -0.63& -0.32& -0.81& 1.69& 0.00& 0.00& 0.00& 0.00\\ 0.00& 0.00& -0.79& -0.08& -0.78& 1.33& 0.00& 0.00& 0.00\\ 0.00& 0.00& 0.00& -0.65& -0.31& -0.22& 1.20& 0.00& 0.00\\ 0.00& 0.00& 0.00& 0.00& -0.59& -0.35& -1.06& 1.19& 0.00\\ 0.00& 0.00& 0.00& 0.00& 0.00& -0.75& -0.14& -1.19& 0.00 \end{bmatrix}$ The right-down entry is zero by the LDU-decomposition, so the matrix Q is only positive semidefinite( one eigenvalue is zero). Some software-cholesky-procedures might not be able to deal with close-to-zero or zero eigenvalues.