- #1
vibe3
- 46
- 1
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:
[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.
[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.