I'm struggling with how to draw phase portrait with purely imaginary complex eigenvalues. I know that the phase portrait should be ellipses but I'm not sure how to determine how exactly the ellipses look like. In the lecture slide, we used the technique of finding the eigenvectors of B (I have attached a screenshot). Is this the only method to determine how exactly the ellipses look like? There is an example provided in one of the tutorials, where the sidenotes say we should "project the eigenvectors to real parts" (I have also attached a screenshot) but I don't quite understand what it means. Any help is appreciated! Thanks!
