### Linear Algebra : Modules, Linear Operators, Characteristic and Minimal Polynomials, Generators, Abelian Groups and Annihilators

Let F be a field and . Then is an n - dimensional vector space over F. Define a function by . (a) Show that T is a linear operator. (b) Find the characteristic and minimal polynomials for T, with explanation. (For the characteristic polynomial, recall that you will need to choose a basis for , find the matrix of T