Author Topic: Drawing phase portrait with complex eigenvalues question  (Read 587 times)

Jessica Wang

  • Newbie
  • *
  • Posts: 1
  • Karma: 0
    • View Profile
Drawing phase portrait with complex eigenvalues question
« on: November 26, 2020, 06:46:11 PM »
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!

Victor Ivrii

  • Administrator
  • Elder Member
  • *****
  • Posts: 2563
  • Karma: 0
    • View Profile
    • Personal website of Victor Ivrii
Re: Drawing phase portrait with complex eigenvalues question
« Reply #1 on: December 01, 2020, 08:46:13 PM »
"How ellipses wouls look like" means the directions and relative size of their semi-axis. See frame 4 of MAT244_W8L3 handout