There is a Lemma in paper "team decision problems" by Radner: Lemma: If $C$ is a $K \times K$ symmetric positive semi-definite matrix, partitioned symmetrically into blocks $C_{ij}$ such that $C_{ii}$ is positive definite for every $i$, and if $Q$ is an $N \times N$ symmetric positive definite matrix with elements $q_{ij}$, then matrix $H$ composed of blocks $q_{ij}C_{ij}$ is positive definite.
Based on this lemma, it has concluded that the linear system: $\sum_{j=1}^N Q_{ij}A_j S_{ji}= W_i$ for $i=1,...,N$, where $Q$ and $S$ matrices are positive definite, has a unique solution for $A_i$'s. In other words, the coefficients of $A_j$ in the equation are positive definite. Can any body tell me how we can conclude this from the Lemma?
Thanks