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April 20th, 2013, 07:33 PM   #1
Joined: Apr 2013

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Prove the Lyapunov equation

The matrix satifies the following Lyapunov equation

prove that necessary and sufficient condition generating a symmetric and positive determined is that all of the eigen values of should be negative.
(Hints: rewritten in the Jordan normal form, one can easily prove the proposition)
But I still cannnot figure it out with the hints!waiting for your excellent proof!
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