Constructing Lyapunov functions using eigenvectors

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1670frank
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Homework Statement



How can I produce a Lyapunov function using the eigenvalues and vectors
x'=-x+y
y'=-x

Homework Equations





The Attempt at a Solution

So I got the matrix using jacobian and I got the matrix
-1 1
-1 0
then i found the eigenvalues to be λ_1= (-1+sqrt3 i)/2 and λ2= (-1-sqrt3 i)/2 and i found the eigenvectors v1= (1 1/2 +sqrt3i /2) v2= (1 1/2 -sqrt3i/2) I am not exactly sure how I can proceed further though. I am not sure how to construct Lyapunov function using this information...
 

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