Hello everybody, I have a question for which I cannot find the answer around, any help would be really appreciated. Suppose we have a matrix A of a linear transformation of a vector space, with only one eigenvalue, say 's'. My question is: Is the operator (A-sI) nilpotent? ('I' is the identity matrix). I am trying to understand the proof of the Jordan Canonical Form Theorem and there is a fuzzy point in my notes about that... Thanks a lot in advance.. EDIT: I am becoming pretty sure about that, but some confirmation would be great..