Is there a basis-free formulation of Jordan normal form theorem?
From some search I did in Google, the answer is apparently yes. But I didn't find any article that I could understand. (I've only taken two semester course in linear algebra.)
My curiosity comes from the question whether the theorem can be generalized to infinite dimensional situation. If it's a separable Hilbert space, we can still represent the linear operator as a matrix, but does the theorem remain true?
In case of non-separable space, I think there's no way to put the linear operator in matrix form. So we need to find a basis-free formulation.
Wikipedia says that there is an analogue of Jordan normal form theorem for compact operators in Banach space. What is this analogous result?