# linear algebra

## Interpreting Complex Eigenvalues of Real Matrices

Introduction Setup The easy case (all eigenvalues are real) The hard case (complex eigenvalues) Demonstration Conclusions References Introduction Lately, I’ve been stuck in getting an intuition for exactly what is going on when a real matrix has complex eigenvalues (and complex eigenvectors) accordingly. After consulting various sources, and playing around with some examples, I think I have a grasp on what’s going on, and translating the math into an interpretation in the original space.