Suppose I have the equation $$A^\top K +KA+Q=0$$ I know that $A$ is stable and $Q$ is symmetric. I want to prove that the solution $K$ to this equation is unique. What constraints should I put on $Q$? How can I prove the uniqueness of the solution?
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Are you solving this equation for $K$? – Ben Grossmann Nov 30 '16 at 15:43
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Yes I am. I will edit the question – cholo14 Nov 30 '16 at 15:45
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According to wikipedia, if $A$ is stable, then the equation will have a unique solution for any $Q$. – Ben Grossmann Nov 30 '16 at 15:45