Are there any special properties of real matrices (not necessarily symmetric) with "real" distinct eigenvalues, other than the well-known properties like being diagonalizable, which has nothing to do with the realness of the eigenvalues?
In short, I'm searching for the properties that comes from the realness of the eigenvalues. Can you at least suggest me a reference for the topic?
Note: This is a little different from the question What do real eigenvalues imply for a matrix as MorganRodgers pointed out in the comments. My question requires that the eigenvalues be distinct and the answer relies on that.