# Toronto Math Forum

## MAT244--2020F => MAT244--Lectures & Home Assignments => Chapter 7 => Topic started by: Jessica Wang on November 26, 2020, 06:46:11 PM

Title: Drawing phase portrait with complex eigenvalues question
Post by: Jessica Wang 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!
Title: Re: Drawing phase portrait with complex eigenvalues question
Post by: Victor Ivrii 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