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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 two quadratic matrix equations [closed]

Given $10 \times 10$ matrices $A$ and $B$, I would like to find $10 \times 10$ matrix $X$ such that $$A = X B X^T \tag{1}$$ $$B = X A X^T \tag{2}$$ How can I solve the issue? if there is a way to solv …
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