I am wondering if anybody knows any reference/idea that can be used to adress the following seemingly simple question
"Is there any set of conditions so that all the eigenvalues of a real positive definite matrix are different?"
Motivation Duality in principal component analysis
Best Answer
One sufficient condition is that the Gersghorin discs associated with a given matrix do not intersect. This is easy to check in practical applications, since one can just compute the discs from the entries of the matrix itself.