Under what conditions on the matrix A can the linear differential equation dx/dt = Ax where x = (x1,x2....,xn)^T have periodic solutions?
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If and only if the matrix A has pure imaginary eigenvalues.
Originally Posted by HallsofIvy If and only if the matrix A has pure imaginary eigenvalues. Is that the only condition? A 4 mark question thought it would have abit more to it
Originally Posted by NFS1 Is that the only condition? A 4 mark question thought it would have abit more to it You are probably expected to prove this result...
Originally Posted by Prove It You are probably expected to prove this result... How would i prove that they have pure imaginary eigenvalues? :S
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Originally Posted by HallsofIvy 
