Originally Posted by
robeuler Let V be a finite dimensional vector space over the field F, with dim(V)=n. We know that End(V), the space of linear transformations from V to itself. dim(End(V)) is n^2.
The minimal polynomial of a linear transformation T is the unique monic polynomial which generates the ideal Ann(V) in F[x]. This polynomial divides the characteristic polynomial of T. Since the degree of the characteristic polynomial is n, the minimal polynomial is at most degree n.
I am asked to prove that the minimal polynomial of T has at most degree n^2, using that End(V) has dimension n^2. So I am asked to prove a weaker bound on the degree than I already know is true.