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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 $Ax=b$.

2 votes

Matrix equation $P^TAP=A$

Using the vec operator, any matrix $X$ such that $vec A$ is an eigenvector of $(X\otimes X)^T$ corresponding to the eigenvalue $1$ would work.
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