Remark 15

Suppose that the conditions of No. 3 are satisfied. Show that every positive Hermitian matrix $H$ over $A$ can be written in the form $LL^*$, where $L = (\lambda_{ij})$ has only zeros below its diagonal and diagonal terms belonging to $K$ and $\geqslant 0$; moreover $L$ is uniquely determined by these conditions when $H$ is invertible (cf. exerc. 10 d) and 7 c)).