Hello, if I have some given vector [itex]c \in R^n[/itex], then I want to find solutions [itex]X \in R^{n\times n}[/itex] to the following equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

X C X^T = C

[/tex]

where [itex]C = c c^T[/itex]. Certainly [itex]X = I[/itex] is a solution, but I'm looking for any nontrivial solutions. We can also assume [itex]X[/itex] is invertible if that helps.

This equation seems related to the Sylvester equation. If the solution is nontrivial, I would appreciate if someone could point me in the direction of any work which has been done on this type of equation.

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# I Can this matrix equation be solved?

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