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Equations whose unknown is a matrix, such as, for instance, algebraic Riccati equations $XAX+XB+CX+D=0$ or matrix differential equations (e.g. $\dot X(t)=AX(t)$. This tag is *not* meant for general systems of linear equations $Ax=b$.
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Solving a "reversed" Stein equation
I am considering the previous version of your question which contained two parts.
Part 1) We assume $Q<P$ which means that $P-Q$ is a strictly positive matrix. Of course this condition is a …