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This question is about equations where the unknown itself is a matrix such as Sylvester or Riccati equations. For systems of linear equations (where the unknown is a vector), use "linear-system".
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Libraries for solving Lyapunov's equation
The following matrix equation
$$B\Sigma + \Sigma B^T + C = 0$$
in $\Sigma$ $-$ for given $B$ and $C$ matrices $-$ appears in my work as a characterization of a covariance matrix. I have learned that …