I'm relatively new to linear algebra and so far I'm aware of at least three types of (real valued) matrices where we can get a guarantee about where the eigenvalues live.
Symmetric ($A^T = A $) $\lambda \in \mathbb{R}$
Skew-Symmetric ($A^T = -A $) $\lambda \in \mathbb{C}$ where Re{$\lambda$}$=0$
Orthogonal ($Q^TQ=I$) $\lambda \in \mathbb{C}$ where $|\lambda|=1$
I'm curious whether there are many other examples of real matrix types (that aren't subsets of the types listed above) where we get similar guarantees about where their eigenvalues sit in the complex plane. (For example, is there a type of real valued matrix that is neither symmetric, skew symmetric, nor orthogonal, but whose eigenvalues can still be proven to lie on the unit circle?) Thanks!
