Need a code using power sequences and eigenvalues to from an elliptical path in MATLAB

I want to know how demonstrate points moving along an elliptical path (like an orbit) in MATLAB. I believe this process uses complex vector as well.

In the book, Elementary Algebra with Applications (Chapter 5.3), they demonstrate how eigenvectors and eigenvalues can be used to from elliptical paths below:

This however is only the theory behind how eigenvectors can form such paths and I'd to see a MATLAB code that generates this using eigenvectors and values. Any other MATLAB applications using this eigenvalue sequence would be fine too.

Thanks.