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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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Is there a method to solve a non-linear quadratic matrix equation?

I am interested in solving the following quadratic equation: $$x^{\top} A x = \sqrt{x^{\top} B x}$$ Here, $x \in \mathbb{R^q}$ is an unknown vector, and A and B are two q$\times$q-dimensional symmetri …
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