# Constructing Lyapunov functions using eigenvectors

1. Jun 6, 2013

### 1670frank

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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) Im not exactly sure how I can proceed further though. Im not sure how to construct Lyapunov function using this information...