My Math Forum Prove the Lyapunov equation

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 April 20th, 2013, 06:33 PM #1 Newbie   Joined: Apr 2013 Posts: 3 Thanks: 0 Prove the Lyapunov equation The matrix $\mathbf{B}$ satifies the following Lyapunov equation $\mathbf{A}^{T}\mathbf{B}+\mathbf{BA}=-\mathbf{I}$ prove that necessary and sufficient condition generating a symmetric and positive determined $\mathbf{B}$ is that all of the eigen values of $\mathbf{A}$ should be negative. (Hints: rewritten $\mathbf{A}$ 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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