is it true that
I observed that if
then some kind of comparative theorem can be used. However, there is no non-trivial solution for this.
If the above proposition is incorrect, could you give me a counterexample?
Assessing stability or instability of a system of equations with complex eigenvalues
Having this system , we get clearly two complex eigenvalues. If one has to assess the stability of the system at these eigenvalues, we have for the matrix A:
that , where , while . But with complex eigenvalues , T which must be real, becomes complex and is always 0, when it would vary from greater than or lesser than zero for real eigenvalues. How do we solve this with complex eigenvalues?