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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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Solution of a quadratic matrix equation with singular coefficent

I have the following quadratic matrix equation in symmetric positive semidefinite covariance matrix $\mathbf{C}$ $$\mathbf{C}\mathbf{S}\mathbf{C}+\mathbf{C}+\mathbf{A}=\mathbf{0}$$ where $\mathbf{S} …